Statistics

Problem 1

Calculate the Interquartile Range (IQR) for the two columns of data: $\{0, 5, 11, 14, 15, 19, 20, 20, 26, 33, 33, 34\}$ and $\{7, 8, 14, 15, 24, 27, 29, 30, 32, 45, 49\}$ .

See Solution

Problem 2

Given a data set with 3 points, and 2 residuals of -12 and 6, find the third residual.

See Solution

Problem 3

Find the winner of the election with 2, 15, and 14 voters, where the 1st, 2nd, and 3rd choices are $A$ , $B$ , and $C$ , using Pairwise Comparison (Copeland's) method.

See Solution

Problem 4

Compute the mean, median, and mode of concrete strengths (in psi) from 9 randomly selected casts: 3950, 4100, 3200, 3000, 2940, 3830, 4100, 4050, 3680. The mean is $\square$ psi, the median is $\square$ psi, and the mode is $\square$ psi.

See Solution

Problem 5

Test if $3\%$ of patients treated with a drug develop nausea as an adverse reaction, using a $0.10$ significance level. Identify the null and alternative hypotheses.

See Solution

Problem 6

Find the score in the 70th percentile of a dataset with mean $\mu=79.22$ and standard deviation $\sigma=7.97$ using the Z-score formula $Z = \frac{X - \mu}{\sigma}$ .

See Solution

Problem 7

Pea genetics experiment: Construct 95% CI for % yellow peas. Does 25% yellow contradict results? Express % in decimal form.

See Solution

Problem 8

Test if more than 91% of acid reflux patients are healed in 8 weeks using drug. $\alpha=0.01$ . Find test statistic $z_0=0.72$ and P-value.

See Solution

Problem 9

Find the average weight of 7 cats with weights $7, 11, 6, 11, 7, 7, 11$ pounds. Round the result to the nearest tenth.

See Solution

Problem 10

Test whether there is a significant difference between the IQs of spouses, given IQ data for 9 married couples. Assume the paired difference distribution is approximately normal. Use a 0.10 significance level.

See Solution

Problem 11

Test claim that SAT prep course increases scores by >60 points on avg. 9 students, $H_0$ : $\mu_1 - \mu_2 \leq 60$ , $\alpha = 0.10$ , normal distribution.

See Solution

Problem 12

Find the margin of error and sample mean using the given $95\%$ confidence interval $(1.58, 2.06)$ . The margin of error is $\$0.24\$. The sample mean is$ \$1.82\$.

See Solution

Problem 13

Determine the type of hypothesis test given $H_0: \sigma=6.9$ and $H_a: \sigma \neq 6.9$ .

See Solution

Problem 14

Find the margin of error for $c=0.95$ , $s=4$ , and $n=8$ .

See Solution

Problem 15

Test whether the mean retirement age of women executives is different from the reported 62.7 years, given a sample of 80 with $\sigma = 4.7$ years.
$\begin{array}{l} H_{0}: \mu = 62.7 \\ H_{a}: \mu \neq 62.7 \end{array}$

See Solution

Problem 16

Evaluate the formula $\chi^{2}=\frac{(n-1) s^{2}}{\sigma^{2}}$ given $\sigma=1.57, n=40, s=3.23$ . Round $\chi^{2}$ to three decimal places.

See Solution

Problem 17

Find the decibel level of a noise that produces $2.72 \times 10^{-5}$ watt/m $^2$ of power, given the formula $\mathrm{D}=10 \mathrm{log}\left(\mathrm{S} / \mathrm{S}_{0}\right)$ where $\mathrm{S}_{0}$ is $10^{-12}$ watt/m $^2$ . (Round to the nearest decibel.)

See Solution

Problem 18

Determine if the following are valid statistical questions: a) How much money do high-school students typically carry? b) How many quarters equal $\$10$ ?

See Solution

Problem 19

Find the probability that a standard normal random variable $z$ is less than 0.24 or greater than or equal to -0.42.

See Solution

Problem 20

After 100 hours, the fractional part of the battery $B$ still operating is $5^{-0.01 \cdot 100} = 0.368$ .

See Solution

Problem 21

Find the probability that a random sample of size $n=61$ drawn from a normal distribution with $\mu=176.7$ and $\sigma=57.5$ has a mean between $166.4$ and $187.7$ .

See Solution

Problem 22

Find the five-number summary and interquartile range for the ages of $11$ physics teachers: $29, 30, 32, 34, 45, 45, 47, 50, 50, 54, 55$ . Five-number summary: Minimum, Lower quartile, Median, Upper quartile, Maximum. Interquartile range.

See Solution

Problem 23

Find the probability that a randomly selected thermometer reading is less than $-1.507$ Celsius, given the readings are normally distributed with $\mu = 0$ Celsius and $\sigma = 1.00$ Celsius.

See Solution

Problem 24

List the sample in ascending order, use comma to separate. Find the range, number of classes, and class width. Complete the frequency distribution by listing the lower and upper class limits for each class and its frequency, including the maximum value(s) to the last class if the limits don't include it/them.

See Solution

Problem 25

Find the mean of the movie counts reported by 7 students: $\frac{13 + 12 + 7 + 13 + 13 + 9 + 16}{7}$ . Round the result to the nearest tenth.

See Solution

Problem 26

Find the range of the number of people who took the daily sightseeing trip around Florence over 9 summer days, where the number of people was $21, 26, 38, 47, 43, 18, 46, 21, 18$ .

See Solution

Problem 27

Find the mean score of $6$ students with scores $90$ , $17$ students with scores $80$ , and $13$ students with scores $70$ . Round the answer to at least one decimal place.

See Solution

Problem 28

Find $P(X=19)$ for the given sampling distribution: $X = \{-16, -12, -7, 10, 19\}$ and $P(X)= \{1/100, 1/50, 9/100, 3/50, \text{?}\}$ .

See Solution

Problem 29

Find the coefficient of variation for a set of $10$ systolic and diastolic blood pressure measurements (in $\mathrm{mm} \mathrm{Hg}$ ). The coefficient of variation for the systolic measurements is $\square \%$ .

See Solution

Problem 30

Compute the correlation coefficient $r$ given $\sum x=5,811, \sum x^{2}=5,632,643, \sum y=578, \sum y^{2}=65,292$ and $\sum x y=553,170$ . Does $r$ imply that $y$ should tend to increase, decrease, or remain constant as $x$ increases?

See Solution

Problem 31

Find the mean of a dataset with $S^{2}=10$ , $n=30$ , and $\sum x^{2}=3290$ .

See Solution

Problem 32

Determine the constant $k$ that makes the given density function $f(x)$ a valid probability density function for the measurement error $X$ .

See Solution

Problem 33

Find the probability that a randomly chosen resident with a master's degree is aged 50 or over, rounded to the nearest thousandth.

See Solution

Problem 34

Determine the number of situps a person who watches $11.5$ hours of TV can do, given the linear regression $y =$ - $0.848x + 31.273$ with $r^2 = 0.614656$ and $r = -0.784$ .

See Solution

Problem 35

Find the critical value $z_{0.03}$ for a 3% significance level.

See Solution

Problem 36

Rainfall in a region is normally distributed with $\mu=42.3$ inches, $\sigma=5.6$ inches. Find percentages of years with rainfall: a) $<44$ inches b) $>39$ inches c) between 38 and 43 inches.

See Solution

Problem 37

Find the third quartile for the given data: $87, 10, 50, 74, 83, 70, 25, 64, 47, 97, 15, 20, 68, 3, 23$ .

See Solution

Problem 38

Find the area under the normal curve to the right of an IQ score of $86$ , given a mean of $100$ and a standard deviation of $15$ . Round the answer to four decimal places.

See Solution

Problem 39

Confirm if $\sum X \cdot f = 18$ for the given distribution of scores: $X = \{4, 3, 2, 1\}$ and $f = \{1, 2, 3, 2\}$ .

See Solution

Problem 40

Determine if the mean tuition of private colleges in California exceeds $\$35,000$ using a one-tailed $t$ -test with $\alpha=0.05$ . $H_0: \mu \leq \$35,000$ $H_a: \mu > \$35,000$

See Solution

Problem 41

Find the class with the least number of social interactions among the classes with the greatest frequency.
$10-14$ , $15-19$ , and $20-24$ have the greatest frequency of 19. Among these, $10-14$ has the least number of social interactions.

See Solution

Problem 42

Using the normal distribution, find the percentage of buyers who paid between $\$14,000$ and $\$18,000$ for a car with mean $\$18,000$ and standard deviation $\$2,000$ .

See Solution

Problem 43

Estimate the mean water usage in gallons per day for a small town, with a maximum error of 0.15 gallons and 80% confidence. Given that the standard deviation is 2.3 gallons and the mean is 17.6 gallons, determine the required sample size.

See Solution

Problem 44

Calculate the first quartile, third quartile, mean, median, range, standard deviation $s$ , interquartile range, lower and upper limits for outliers, and variance $s^2$ for the given GPA data of 15 students, rounded to 4 decimal places.

See Solution

Problem 45

Find the best predicted value of the response variable for $x=3.5$ given $r=0.742$ and the regression equation $\hat{y}=55.8+2.79x$ . Round to two decimal places. Use a significance level of 0.05.

See Solution

Problem 46

Compute the regression line equation for a dataset with $\bar{x}=9$ , $s_{x}=1$ , $\bar{y}=682$ , $s_{y}=51$ , $r=-0.71$ . Round $a$ and $b$ to two decimal places.

See Solution

Problem 47

Design an assembly work table with sitting knee height range between $5^{th}$ percentile women and $95^{th}$ percentile men. Male sitting knee height $\sim \mathcal{N}(21.7\text{ in}, 1.2^2\text{ in}^2)$ , Female $\sim \mathcal{N}(19.2\text{ in}, 1.1^2\text{ in}^2)$ . Find minimum table clearance to fit $95\%$ of men.

See Solution

Problem 48

Compare the z-scores of the tallest ( $230$ cm) and shortest ( $136.6$ cm) men, given a mean of $175.78$ cm and standard deviation of $6.01$ cm. The man with the more extreme z-score had the more extreme height.

See Solution

Problem 49

Which $r$ -value is not possible? A) 0.5, B) 1.2, C) -0.1, D) -0.75

See Solution

Problem 50

Determine which company has the least salary variability and the lowest average salaries based on the given salary ranges and means: Company A: range $\$ 47,000$ , mean $\$ 37,000$ Company B: range $\$ 56,000$ , mean $\$ 38,000$ Company C: range $\$ 50,000$ , mean $\$ 43,000$ Company D: range $\$ 48,000$ , mean $\$ 34,000$

See Solution

Problem 51

Determine if the average weight of babies born in a week is a discrete or continuous variable.

See Solution

Problem 52

Find the missing values in the relative frequency table for the concession stand sales data. Solve for variables $a$ , $b$ , $c$ , $d$ , and $e$ to complete the table.

See Solution

Problem 53

Find the standard error of the sample mean for the daily high temperatures (in $\degree$ F) in Des Moines over 1 week: Monday (64.5), Tuesday (64), Wednesday (66.5), Thursday (64), Friday (62.5), Saturday (61), Sunday (63).

See Solution

Problem 54

Find the mean of the following set of numbers: $8, 9, 5, 8, 3, 7, 3, 9, 2$ .

See Solution

Problem 55

Calculate the 7-point moving average (MA) value for $T$ on the Saturday of week 2.

See Solution

Problem 56

There is no mode when all data values are distinct. True or False?

See Solution

Problem 57

The average grocery spending for Palestinian households is 600 NIS/week with a standard deviation of 120 NIS. What is the percentage of households spending more than 850 NIS/week? What is the probability a household spends 600 NIS/week? What is the maximum spending for a thrifty shopper household (1st quartile)?
$5.94\%$ , 1, 519.6 NIS

See Solution

Problem 58

Find the third quartile for the set of lengths: 130, 170, $160, 160, 150, 190$ .

See Solution

Problem 59

Determine if the data describing the number of murders in different cities in a year are discrete or continuous, and explain why.
$A. \text{The data are continuous because the data can take on any value in an interval.}$ $B. \text{The data are continuous because the data can only take on specific values.}$ $C. \text{The data are discrete because the data can take on any value in an interval.}$ $D. \text{The data are discrete because the data can only take on specific values.}$

See Solution

Problem 60

What percentage of students from a high school with normally distributed SAT scores (mean $1497$ , std. dev. $310$ ) meet the college's minimum score requirement of $536$ ?

See Solution

Problem 61

Find the outlier in a data set with 25th percentile 13.5 and 75th percentile 18.2. Options: a) 24.78, b) 6.54, c) $6.42$ , d) 20.17, e) None.

See Solution

Problem 62

Find the probability of a standard normal random variable $z$ being between -1.65 and 0. Round the answer to four decimal places.

See Solution

Problem 63

Create a box plot with min and max as whiskers for the data: $2, 27, 8, 26, 26, 3, 29, 18, 34, 19, 21$ .

See Solution

Problem 64

Survey of 2017 U.S. adults, 383 said FDR was best president since WWII. Find probability that 2 randomly selected adults both say FDR was best. P(both say FDR) = $\frac{383}{2017} \cdot \frac{382}{2016}$ .

See Solution

Problem 65

Find the probability that a randomly selected portable MP3 player from Company XYZ will have a replacement time less than 1.2 years, given the replacement times are normally distributed with $\mu=3.7$ years and $\sigma=1$ year.

See Solution

Problem 66

Find the probability, rounded to the nearest hundredth, that a citizen who moved in 2004 was a person who moved to a different country. The table shows the number, in millions, of movers categorized by ownership status and region moved to.

See Solution

Problem 67

Find the margin of error for a poll of 130 people, where $64\%$ said they liked dogs, at a $90\%$ confidence level.

See Solution

Problem 68

Find the mean $\mu_{\bar{x}}$ and standard deviation $\sigma_{\bar{x}}$ of the sample mean, given population mean $\mu=83$ , population standard deviation $\sigma=24$ , and sample size $n=36$ .

See Solution

Problem 69

A study found that a new sneaker increased the average jump height of 32 male athletes by $1.45 \pm 0.91$ inches. What is the $95\%$ confidence interval margin of error for the average jump increase?

See Solution

Problem 70

Find the line of best fit for the data: $\{(2, 10), (4, 13), (4, 12), (6, 15), (8, 17), (10, 20)\}$ . The equation of the line is $y = \square x + \square$ .

See Solution

Problem 71

Find the mode of the set of numbers: $89, 84, 61, 27, 95, 39, 7, 86, 59, 7, 40, 45, 80, 32, 49$ .

See Solution

Problem 72

Analyze gender gap in political beliefs and party ID. Identify response and explanatory variables. Calculate proportions of male/female Republicans. $\frac{83}{369}$ male Republicans, $\frac{98}{551}$ female Republicans.

See Solution

Problem 73

Compute the sum of 33 times each of the 11 measurements: $\sum_{i=1}^{11} 33 x_{i}$

See Solution

Problem 74

Determine the appropriate problem-solving method to find the five-number summary and draw a box-and-whisker plot for the given data: $7, 21, 28, 18, 29, 31, 47, 18, 40, 29, 32, 36, 48, 46, 55$ .

See Solution

Problem 75

Probability that a randomly selected teacher in Connecticut makes less than $54,500 per year.$ $P(X < 54,500) = \Phi \left( \frac{54,500 - 57,337}{7,500} \right) \approx \square$ $

See Solution

Problem 76

Find the number of students who chose Drama, Other, or Historical genres from a college with 15,000 students, given the percentages: $27\%$ Drama, $23\%$ Other, and $20\%$ Historical.

See Solution

Problem 77

Find the critical value(s) for the left-tailed $t$ -test with $\alpha=0.025$ and $n=27$ . The critical value(s) is/are $t_{\alpha, n-1}$ .

See Solution

Problem 78

Construct a 99% confidence interval for the mean body temperature of 105 healthy adults with $\bar{x}=98.7^{\circ}F$ and $s=0.64^{\circ}F$ . Does the interval suggest the use of $98.6^{\circ}F$ as the mean body temperature?
A. The interval suggests the mean could be $98.6^{\circ}F$ . B. The interval suggests the mean is higher than $98.6^{\circ}F$ . C. The interval suggests the mean is lower than $98.6^{\circ}F$ .

See Solution

Problem 79

Find the proportion of steel rods with length less than $24.9 \mathrm{cm}$ , given the rods have a mean length of $25 \mathrm{cm}$ and standard deviation of $0.07 \mathrm{cm}$ .

See Solution

Problem 80

An elevator has a capacity of 2385 lb for 15 passengers. Find the probability that 15 adult males with $\mu = 165$ lb, $\sigma = 32$ lb have a mean weight > 159 lb, indicating an overload. Does the elevator appear safe?

See Solution

Problem 81

Predict Janelle's final exam score using the linear regression equation $\hat{y}=11+0.5\mathrm{x}$ where $\mathrm{x}=90$ . Calculate the residual between the predicted and actual final exam scores.

See Solution

Problem 82

Determine the values of $\hat{p}, \hat{q}, n, E$ , and $p$ in a poll of 500 adults about favorite pie, where 11% chose chocolate pie with a margin of error of ±4 percentage points and a 95% confidence level.

See Solution

Problem 83

Find the $t$ -value with 12 degrees of freedom such that the right-tailed area is 0.05. Round to 3 decimal places.

See Solution

Problem 84

Redefine a claim's complement and identify $H_0$ and $H_a$ . The claim is $\mu \geq 508$ . The complement is $\mu < 508$ . $H_0: \mu \geq 508$ , $H_a: \mu < 508$ .

See Solution

Problem 85

Determine the 90% confidence interval for the true mean weight of a population of dogs, given the sample mean of 69 ounces and population standard deviation of 5.1 ounces.

See Solution

Problem 86

Monthly rents of 10 people change when one person's rent decreases from $1630 to$ 1230. How does the median and mean change?

See Solution

Problem 87

Find the five-number summary for the gold, silver, and bronze medals won by 19 countries at the 2012 London Olympics: $1, 3, 7, 13, 46$ (gold), $1, 5, 9, 16, 29$ (silver), and $4, 7, 9, 12, 32$ (bronze).

See Solution

Problem 88

What is the formula to find a weighted mean? $\frac{\Sigma w \cdot x}{\Sigma w}$

See Solution

Problem 89

Find the P-value for a right-tailed test with test statistic $z=0.52$ . Use a 0.05 significance level to determine if the null hypothesis should be rejected or failed to be rejected.

See Solution

Problem 90

Find the $z$ -score where the area to its right under the standard normal distribution is 0.39. Round the answer to 4 decimal places.

See Solution

Problem 91

Find the 28th percentile, middle 96% range, and interquartile range for the number of chocolate chips in a bag, where the number is approximately normally distributed with $\mu=1262$ and $\sigma=118$ .

See Solution

Problem 92

Interpret the coefficient of determination $r^2 = 0.8744932359$ and explain its meaning.

See Solution

Problem 93

Which statement about a negatively skewed distribution's density curve is true? $A. \text{Right tail is longer than left}$ $B. \text{Left and right tails are equal}$ $C. \text{Left and right sides are mirror images}$ $D. \text{Left tail is longer than right}$

See Solution

Problem 94

A study of 1000 people tested a new pain medication. One group received the medication, the other a $\text{placebo}$ . This is a $\text{double-blind}$ experiment.

See Solution

Problem 95

Encuentra la media de los números $2, 3, 5, 6, 8, 8, 11$ dividiendo su suma entre $2+3+5+6+8+8+11$ .

See Solution

Problem 96

Find the 10th percentile of the number of cars sold per week by the 65 car salespersons. The data shows that 14 sell 5 cars, 19 sell 6 cars, 12 sell 7 cars, 9 sell 8 cars, and 11 sell 9 cars.

See Solution

Problem 97

Estimate the true mean weight of all chocolates produced by a machine with a $99\%$ confidence interval, given a sample of 18 chocolates with mean $3.1$ grams and standard deviation $0.09$ grams.

See Solution

Problem 98

Raleigh has 10,500 registered voters. A poll of 200 voters showed $119$ for Brown, $77$ for Feliz, and $4$ undecided. Find the expected number of voters for each candidate and undecided.

See Solution

Problem 99

Test if the percentage of commercial truck drivers with sleep apnea is not $3.5\%$ , using a sample of 308 drivers with 19 cases. Use a 0.05 significance level.

See Solution

Problem 100

Use the empirical rule to estimate the number of farms with land and building values per acre between $\$ 1300$ and $\$ 2100$ , given a sample of 72 farms with mean $\$ 1700$ and standard deviation $\$ 200$ .

See Solution

1 2 3

Statistics

Problem 1

Problem 2

Given a data set with 3 points, and 2 residuals of -12 and 6, find the third residual.

Problem 3

Find the winner of the election with 2, 15, and 14 voters, where the 1st, 2nd, and 3rd choices are AAA, BBB, and CCC, using Pairwise Comparison (Copeland's) method.

Problem 4

Compute the mean, median, and mode of concrete strengths (in psi) from 9 randomly selected casts: 3950, 4100, 3200, 3000, 2940, 3830, 4100, 4050, 3680. The mean is □\square□ psi, the median is □\square□ psi, and the mode is □\square□ psi.

Problem 5

Test if 3%3\%3% of patients treated with a drug develop nausea as an adverse reaction, using a 0.100.100.10 significance level. Identify the null and alternative hypotheses.

Problem 6

Find the score in the 70th percentile of a dataset with mean μ=79.22\mu=79.22μ=79.22 and standard deviation σ=7.97\sigma=7.97σ=7.97 using the Z-score formula Z=X−μσZ = \frac{X - \mu}{\sigma}Z=σX−μ​.

Problem 7

Pea genetics experiment: Construct 95% CI for % yellow peas. Does 25% yellow contradict results? Express % in decimal form.

Problem 8

Test if more than 91% of acid reflux patients are healed in 8 weeks using drug. α=0.01\alpha=0.01α=0.01. Find test statistic z0=0.72z_0=0.72z0​=0.72 and P-value.

Problem 9

Find the average weight of 7 cats with weights 7,11,6,11,7,7,117, 11, 6, 11, 7, 7, 117,11,6,11,7,7,11 pounds. Round the result to the nearest tenth.

Problem 10

Test whether there is a significant difference between the IQs of spouses, given IQ data for 9 married couples. Assume the paired difference distribution is approximately normal. Use a 0.10 significance level.

Problem 11

Test claim that SAT prep course increases scores by >60 points on avg. 9 students, H0H_0H0​: μ1−μ2≤60\mu_1 - \mu_2 \leq 60μ1​−μ2​≤60, α=0.10\alpha = 0.10α=0.10, normal distribution.

Problem 12

Find the margin of error and sample mean using the given 95%95\%95% confidence interval (1.58,2.06)(1.58, 2.06)(1.58,2.06). The margin of error is $0.24$.Thesamplemeanis\$0.24\$. The sample mean is $0.24$.Thesamplemeanis\$1.82\$.

Problem 13

Determine the type of hypothesis test given H0:σ=6.9H_0: \sigma=6.9H0​:σ=6.9 and Ha:σ≠6.9H_a: \sigma \neq 6.9Ha​:σ=6.9.

Problem 14

Find the margin of error for c=0.95c=0.95c=0.95, s=4s=4s=4, and n=8n=8n=8.

Problem 15

Test whether the mean retirement age of women executives is different from the reported 62.7 years, given a sample of 80 with σ=4.7\sigma = 4.7σ=4.7 years.H0:μ=62.7Ha:μ≠62.7 \begin{array}{l} H_{0}: \mu = 62.7 \\ H_{a}: \mu \neq 62.7 \end{array} H0​:μ=62.7Ha​:μ=62.7​

Problem 16

Evaluate the formula χ2=(n−1)s2σ2\chi^{2}=\frac{(n-1) s^{2}}{\sigma^{2}}χ2=σ2(n−1)s2​ given σ=1.57,n=40,s=3.23\sigma=1.57, n=40, s=3.23σ=1.57,n=40,s=3.23. Round χ2\chi^{2}χ2 to three decimal places.

Problem 17

Problem 18

Determine if the following are valid statistical questions: a) How much money do high-school students typically carry? b) How many quarters equal $10\$10$10?

Problem 19

Find the probability that a standard normal random variable zzz is less than 0.24 or greater than or equal to -0.42.

Problem 20

After 100 hours, the fractional part of the battery BBB still operating is 5−0.01⋅100=0.3685^{-0.01 \cdot 100} = 0.3685−0.01⋅100=0.368.

Problem 21

Find the probability that a random sample of size n=61n=61n=61 drawn from a normal distribution with μ=176.7\mu=176.7μ=176.7 and σ=57.5\sigma=57.5σ=57.5 has a mean between 166.4166.4166.4 and 187.7187.7187.7.

Problem 22

Problem 23

Find the probability that a randomly selected thermometer reading is less than −1.507-1.507−1.507 Celsius, given the readings are normally distributed with μ=0\mu = 0μ=0 Celsius and σ=1.00\sigma = 1.00σ=1.00 Celsius.

Problem 24

Problem 25

Find the mean of the movie counts reported by 7 students: 13+12+7+13+13+9+167\frac{13 + 12 + 7 + 13 + 13 + 9 + 16}{7}713+12+7+13+13+9+16​. Round the result to the nearest tenth.

Problem 26

Find the range of the number of people who took the daily sightseeing trip around Florence over 9 summer days, where the number of people was 21,26,38,47,43,18,46,21,1821, 26, 38, 47, 43, 18, 46, 21, 1821,26,38,47,43,18,46,21,18.

Problem 27

Find the mean score of 666 students with scores 909090, 171717 students with scores 808080, and 131313 students with scores 707070. Round the answer to at least one decimal place.

Problem 28

Find P(X=19)P(X=19)P(X=19) for the given sampling distribution: X={−16,−12,−7,10,19}X = \{-16, -12, -7, 10, 19\}X={−16,−12,−7,10,19} and P(X)={1/100,1/50,9/100,3/50,?}P(X)= \{1/100, 1/50, 9/100, 3/50, \text{?}\}P(X)={1/100,1/50,9/100,3/50,?}.

Problem 29

Find the coefficient of variation for a set of 101010 systolic and diastolic blood pressure measurements (in mmHg\mathrm{mm} \mathrm{Hg}mmHg). The coefficient of variation for the systolic measurements is □%\square \%□%.

Problem 30

Problem 31

Find the mean of a dataset with S2=10S^{2}=10S2=10, n=30n=30n=30, and ∑x2=3290\sum x^{2}=3290∑x2=3290.

Problem 32

Determine the constant kkk that makes the given density function f(x)f(x)f(x) a valid probability density function for the measurement error XXX.

Problem 33

Find the probability that a randomly chosen resident with a master's degree is aged 50 or over, rounded to the nearest thousandth.

Problem 34

Determine the number of situps a person who watches 11.511.511.5 hours of TV can do, given the linear regression y=y = y=-0.848x+31.2730.848x + 31.2730.848x+31.273 with r2=0.614656r^2 = 0.614656r2=0.614656 and r=−0.784r = -0.784r=−0.784.

Problem 35

Find the critical value z0.03z_{0.03}z0.03​ for a 3% significance level.

Problem 36

Rainfall in a region is normally distributed with μ=42.3\mu=42.3μ=42.3 inches, σ=5.6\sigma=5.6σ=5.6 inches. Find percentages of years with rainfall: a) <44<44<44 inches b) >39>39>39 inches c) between 38 and 43 inches.

Problem 37

Find the third quartile for the given data: 87,10,50,74,83,70,25,64,47,97,15,20,68,3,2387, 10, 50, 74, 83, 70, 25, 64, 47, 97, 15, 20, 68, 3, 2387,10,50,74,83,70,25,64,47,97,15,20,68,3,23.

Problem 38

Find the area under the normal curve to the right of an IQ score of 868686, given a mean of 100100100 and a standard deviation of 151515. Round the answer to four decimal places.

Problem 39

Confirm if ∑X⋅f=18\sum X \cdot f = 18∑X⋅f=18 for the given distribution of scores: X={4,3,2,1}X = \{4, 3, 2, 1\}X={4,3,2,1} and f={1,2,3,2}f = \{1, 2, 3, 2\}f={1,2,3,2}.

Problem 40

Determine if the mean tuition of private colleges in California exceeds $35,000\$35,000$35,000 using a one-tailed ttt-test with α=0.05\alpha=0.05α=0.05. H0:μ≤$35,000H_0: \mu \leq \$35,000H0​:μ≤$35,000 Ha:μ>$35,000H_a: \mu > \$35,000Ha​:μ>$35,000

Problem 41

Find the class with the least number of social interactions among the classes with the greatest frequency.10−1410-1410−14, 15−1915-1915−19, and 20−2420-2420−24 have the greatest frequency of 19. Among these, 10−1410-1410−14 has the least number of social interactions.

Problem 42

Using the normal distribution, find the percentage of buyers who paid between $14,000\$14,000$14,000 and $18,000\$18,000$18,000 for a car with mean $18,000\$18,000$18,000 and standard deviation $2,000\$2,000$2,000.

Find the winner of the election with 2, 15, and 14 voters, where the 1st, 2nd, and 3rd choices are $A$ , $B$ , and $C$ , using Pairwise Comparison (Copeland's) method.

Compute the mean, median, and mode of concrete strengths (in psi) from 9 randomly selected casts: 3950, 4100, 3200, 3000, 2940, 3830, 4100, 4050, 3680. The mean is $\square$ psi, the median is $\square$ psi, and the mode is $\square$ psi.

Test if $3\%$ of patients treated with a drug develop nausea as an adverse reaction, using a $0.10$ significance level. Identify the null and alternative hypotheses.

Find the score in the 70th percentile of a dataset with mean $\mu=79.22$ and standard deviation $\sigma=7.97$ using the Z-score formula $Z = \frac{X - \mu}{\sigma}$ .

Test if more than 91% of acid reflux patients are healed in 8 weeks using drug. $\alpha=0.01$ . Find test statistic $z_0=0.72$ and P-value.

Find the average weight of 7 cats with weights $7, 11, 6, 11, 7, 7, 11$ pounds. Round the result to the nearest tenth.

Test claim that SAT prep course increases scores by >60 points on avg. 9 students, $H_0$ : $\mu_1 - \mu_2 \leq 60$ , $\alpha = 0.10$ , normal distribution.

Find the margin of error and sample mean using the given $95\%$ confidence interval $(1.58, 2.06)$ . The margin of error is $\$0.24\$. The sample mean is$ \$1.82\$.

Determine the type of hypothesis test given $H_0: \sigma=6.9$ and $H_a: \sigma \neq 6.9$ .

Find the margin of error for $c=0.95$ , $s=4$ , and $n=8$ .

Test whether the mean retirement age of women executives is different from the reported 62.7 years, given a sample of 80 with $\sigma = 4.7$ years.
$\begin{array}{l} H_{0}: \mu = 62.7 \\ H_{a}: \mu \neq 62.7 \end{array}$

Evaluate the formula $\chi^{2}=\frac{(n-1) s^{2}}{\sigma^{2}}$ given $\sigma=1.57, n=40, s=3.23$ . Round $\chi^{2}$ to three decimal places.

Determine if the following are valid statistical questions: a) How much money do high-school students typically carry? b) How many quarters equal $\$10$ ?

Find the probability that a standard normal random variable $z$ is less than 0.24 or greater than or equal to -0.42.

After 100 hours, the fractional part of the battery $B$ still operating is $5^{-0.01 \cdot 100} = 0.368$ .

Find the probability that a random sample of size $n=61$ drawn from a normal distribution with $\mu=176.7$ and $\sigma=57.5$ has a mean between $166.4$ and $187.7$ .

Find the probability that a randomly selected thermometer reading is less than $-1.507$ Celsius, given the readings are normally distributed with $\mu = 0$ Celsius and $\sigma = 1.00$ Celsius.

Find the mean of the movie counts reported by 7 students: $\frac{13 + 12 + 7 + 13 + 13 + 9 + 16}{7}$ . Round the result to the nearest tenth.

Find the range of the number of people who took the daily sightseeing trip around Florence over 9 summer days, where the number of people was $21, 26, 38, 47, 43, 18, 46, 21, 18$ .

Find the mean score of $6$ students with scores $90$ , $17$ students with scores $80$ , and $13$ students with scores $70$ . Round the answer to at least one decimal place.

Find $P(X=19)$ for the given sampling distribution: $X = \{-16, -12, -7, 10, 19\}$ and $P(X)= \{1/100, 1/50, 9/100, 3/50, \text{?}\}$ .

Find the coefficient of variation for a set of $10$ systolic and diastolic blood pressure measurements (in $\mathrm{mm} \mathrm{Hg}$ ). The coefficient of variation for the systolic measurements is $\square \%$ .

Find the mean of a dataset with $S^{2}=10$ , $n=30$ , and $\sum x^{2}=3290$ .

Determine the constant $k$ that makes the given density function $f(x)$ a valid probability density function for the measurement error $X$ .

Determine the number of situps a person who watches $11.5$ hours of TV can do, given the linear regression $y =$ - $0.848x + 31.273$ with $r^2 = 0.614656$ and $r = -0.784$ .

Find the critical value $z_{0.03}$ for a 3% significance level.

Rainfall in a region is normally distributed with $\mu=42.3$ inches, $\sigma=5.6$ inches. Find percentages of years with rainfall: a) $<44$ inches b) $>39$ inches c) between 38 and 43 inches.

Find the third quartile for the given data: $87, 10, 50, 74, 83, 70, 25, 64, 47, 97, 15, 20, 68, 3, 23$ .

Find the area under the normal curve to the right of an IQ score of $86$ , given a mean of $100$ and a standard deviation of $15$ . Round the answer to four decimal places.

Confirm if $\sum X \cdot f = 18$ for the given distribution of scores: $X = \{4, 3, 2, 1\}$ and $f = \{1, 2, 3, 2\}$ .

Determine if the mean tuition of private colleges in California exceeds $\$35,000$ using a one-tailed $t$ -test with $\alpha=0.05$ . $H_0: \mu \leq \$35,000$ $H_a: \mu > \$35,000$

Find the class with the least number of social interactions among the classes with the greatest frequency.
$10-14$ , $15-19$ , and $20-24$ have the greatest frequency of 19. Among these, $10-14$ has the least number of social interactions.

Using the normal distribution, find the percentage of buyers who paid between $\$14,000$ and $\$18,000$ for a car with mean $\$18,000$ and standard deviation $\$2,000$ .

Calculate the first quartile, third quartile, mean, median, range, standard deviation $s$ , interquartile range, lower and upper limits for outliers, and variance $s^2$ for the given GPA data of 15 students, rounded to 4 decimal places.

Find the best predicted value of the response variable for $x=3.5$ given $r=0.742$ and the regression equation $\hat{y}=55.8+2.79x$ . Round to two decimal places. Use a significance level of 0.05.

Compute the regression line equation for a dataset with $\bar{x}=9$ , $s_{x}=1$ , $\bar{y}=682$ , $s_{y}=51$ , $r=-0.71$ . Round $a$ and $b$ to two decimal places.

Compare the z-scores of the tallest ( $230$ cm) and shortest ( $136.6$ cm) men, given a mean of $175.78$ cm and standard deviation of $6.01$ cm. The man with the more extreme z-score had the more extreme height.

Which $r$ -value is not possible? A) 0.5, B) 1.2, C) -0.1, D) -0.75

Find the missing values in the relative frequency table for the concession stand sales data. Solve for variables $a$ , $b$ , $c$ , $d$ , and $e$ to complete the table.

Find the standard error of the sample mean for the daily high temperatures (in $\degree$ F) in Des Moines over 1 week: Monday (64.5), Tuesday (64), Wednesday (66.5), Thursday (64), Friday (62.5), Saturday (61), Sunday (63).

Find the mean of the following set of numbers: $8, 9, 5, 8, 3, 7, 3, 9, 2$ .

Calculate the 7-point moving average (MA) value for $T$ on the Saturday of week 2.

Find the third quartile for the set of lengths: 130, 170, $160, 160, 150, 190$ .

What percentage of students from a high school with normally distributed SAT scores (mean $1497$ , std. dev. $310$ ) meet the college's minimum score requirement of $536$ ?

Find the outlier in a data set with 25th percentile 13.5 and 75th percentile 18.2. Options: a) 24.78, b) 6.54, c) $6.42$ , d) 20.17, e) None.

Find the probability of a standard normal random variable $z$ being between -1.65 and 0. Round the answer to four decimal places.

Create a box plot with min and max as whiskers for the data: $2, 27, 8, 26, 26, 3, 29, 18, 34, 19, 21$ .

Survey of 2017 U.S. adults, 383 said FDR was best president since WWII. Find probability that 2 randomly selected adults both say FDR was best. P(both say FDR) = $\frac{383}{2017} \cdot \frac{382}{2016}$ .

Find the probability that a randomly selected portable MP3 player from Company XYZ will have a replacement time less than 1.2 years, given the replacement times are normally distributed with $\mu=3.7$ years and $\sigma=1$ year.

Find the margin of error for a poll of 130 people, where $64\%$ said they liked dogs, at a $90\%$ confidence level.

Find the mean $\mu_{\bar{x}}$ and standard deviation $\sigma_{\bar{x}}$ of the sample mean, given population mean $\mu=83$ , population standard deviation $\sigma=24$ , and sample size $n=36$ .

A study found that a new sneaker increased the average jump height of 32 male athletes by $1.45 \pm 0.91$ inches. What is the $95\%$ confidence interval margin of error for the average jump increase?

Find the line of best fit for the data: $\{(2, 10), (4, 13), (4, 12), (6, 15), (8, 17), (10, 20)\}$ . The equation of the line is $y = \square x + \square$ .

Find the mode of the set of numbers: $89, 84, 61, 27, 95, 39, 7, 86, 59, 7, 40, 45, 80, 32, 49$ .

Analyze gender gap in political beliefs and party ID. Identify response and explanatory variables. Calculate proportions of male/female Republicans. $\frac{83}{369}$ male Republicans, $\frac{98}{551}$ female Republicans.

Compute the sum of 33 times each of the 11 measurements: $\sum_{i=1}^{11} 33 x_{i}$

Determine the appropriate problem-solving method to find the five-number summary and draw a box-and-whisker plot for the given data: $7, 21, 28, 18, 29, 31, 47, 18, 40, 29, 32, 36, 48, 46, 55$ .