Solved on Nov 30, 2023

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.

STEP 1

Assumptions
1. The population proportion (p) of Americans who suffer from sleep apnea is 3.5% or 0.035.
2. The sample size (n) of commercial truck drivers is 308.
3. The number of commercial truck drivers who suffer from sleep apnea in the sample (x) is 19.
4. The level of significance (α) is 0.05.

STEP 2

First, we need to find the sample proportion (p̂). This is the ratio of the number of commercial truck drivers who suffer from sleep apnea in the sample (x) to the sample size (n).
$p̂ = x / n$

STEP 3

Now, plug in the given values for x and n to calculate the sample proportion.
$p̂ = 19 / 308$

STEP 4

Calculate the sample proportion.
$p̂ = 19 / 308 = 0.06168831168831169$

STEP 5

The test statistic for a hypothesis test about a population proportion is a z-score (z). The formula for the z-score is:
$z = (p̂ - p) / √[(p(1 - p)) / n]$

STEP 6

Now, plug in the given values for p̂, p, and n to calculate the z-score.
$z = (0.06168831168831169 - 0.035) / √[(0.035(1 - 0.035)) / 308]$

STEP 7

Calculate the z-score.
$z = (0.06168831168831169 - 0.035) / √[(0.035(1 - 0.035)) / 308] = 2.57$
The test statistic is 2.57.

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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.

STEP 1

Assumptions
1. The population proportion (p) of Americans who suffer from sleep apnea is 3.5% or 0.035.
2. The sample size (n) of commercial truck drivers is 308.
3. The number of commercial truck drivers who suffer from sleep apnea in the sample (x) is 19.
4. The level of significance (α) is 0.05.

STEP 2

First, we need to find the sample proportion (p̂). This is the ratio of the number of commercial truck drivers who suffer from sleep apnea in the sample (x) to the sample size (n).
$p̂ = x / n$

STEP 3

Now, plug in the given values for x and n to calculate the sample proportion.
$p̂ = 19 / 308$

STEP 4

Calculate the sample proportion.
$p̂ = 19 / 308 = 0.06168831168831169$

STEP 5

The test statistic for a hypothesis test about a population proportion is a z-score (z). The formula for the z-score is:
$z = (p̂ - p) / √[(p(1 - p)) / n]$

STEP 6

Now, plug in the given values for p̂, p, and n to calculate the z-score.
$z = (0.06168831168831169 - 0.035) / √[(0.035(1 - 0.035)) / 308]$

STEP 7

Calculate the z-score.
$z = (0.06168831168831169 - 0.035) / √[(0.035(1 - 0.035)) / 308] = 2.57$
The test statistic is 2.57.

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

STEP 1

Assumptions1. The population proportion (p) of Americans who suffer from sleep apnea is 3.5% or 0.035.2. The sample size (n) of commercial truck drivers is 308.3. The number of commercial truck drivers who suffer from sleep apnea in the sample (x) is 19.4. The level of significance (α) is 0.05.

STEP 2

First, we need to find the sample proportion (p̂). This is the ratio of the number of commercial truck drivers who suffer from sleep apnea in the sample (x) to the sample size (n).p^=x/np̂ = x / np^​=x/n

STEP 3

Now, plug in the given values for x and n to calculate the sample proportion.p^=19/308p̂ = 19 / 308p^​=19/308

STEP 4

Calculate the sample proportion.p^=19/308=0.06168831168831169p̂ = 19 / 308 = 0.06168831168831169p^​=19/308=0.06168831168831169

STEP 5

The test statistic for a hypothesis test about a population proportion is a z-score (z). The formula for the z-score is:z=(p^−p)/√[(p(1−p))/n]z = (p̂ - p) / √[(p(1 - p)) / n]z=(p^​−p)/√[(p(1−p))/n]

STEP 6

Now, plug in the given values for p̂, p, and n to calculate the z-score.z=(0.06168831168831169−0.035)/√[(0.035(1−0.035))/308]z = (0.06168831168831169 - 0.035) / √[(0.035(1 - 0.035)) / 308]z=(0.06168831168831169−0.035)/√[(0.035(1−0.035))/308]

STEP 7

Calculate the z-score.z=(0.06168831168831169−0.035)/√[(0.035(1−0.035))/308]=2.57z = (0.06168831168831169 - 0.035) / √[(0.035(1 - 0.035)) / 308] = 2.57z=(0.06168831168831169−0.035)/√[(0.035(1−0.035))/308]=2.57The test statistic is 2.57.

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

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.

First, we need to find the sample proportion (p̂). This is the ratio of the number of commercial truck drivers who suffer from sleep apnea in the sample (x) to the sample size (n).
$p̂ = x / n$

Now, plug in the given values for x and n to calculate the sample proportion.
$p̂ = 19 / 308$

Calculate the sample proportion.
$p̂ = 19 / 308 = 0.06168831168831169$

The test statistic for a hypothesis test about a population proportion is a z-score (z). The formula for the z-score is:
$z = (p̂ - p) / √[(p(1 - p)) / n]$

Now, plug in the given values for p̂, p, and n to calculate the z-score.
$z = (0.06168831168831169 - 0.035) / √[(0.035(1 - 0.035)) / 308]$

Calculate the z-score.
$z = (0.06168831168831169 - 0.035) / √[(0.035(1 - 0.035)) / 308] = 2.57$
The test statistic is 2.57.