Solved on Nov 30, 2023

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\$.

STEP 1

Assumptions
1. The confidence interval is (1.58, 2.06)
2. The confidence interval is symmetric around the sample mean

STEP 2

The confidence interval is defined as the range in which we are confident that the population mean lies. It is symmetric around the sample mean. So, the sample mean is the midpoint of the confidence interval.
$Sample\, mean = (Lower\, limit + Upper\, limit) / 2$

STEP 3

Now, plug in the given values for the lower limit and upper limit to calculate the sample mean.
$Sample\, mean = (1.58 + 2.06) / 2$

STEP 4

Calculate the sample mean.
$Sample\, mean = (1.58 + 2.06) / 2 = 1.82$

STEP 5

The margin of error is defined as the distance from the sample mean to either end of the confidence interval. So, we subtract the sample mean from the upper limit (or subtract the lower limit from the sample mean, the result will be the same due to the symmetry of the confidence interval).
$Margin\, of\, error = Upper\, limit - Sample\, mean$

STEP 6

Now, plug in the given values for the upper limit and the calculated sample mean to calculate the margin of error.
$Margin\, of\, error = 2.06 - 1.82$

STEP 7

Calculate the margin of error.
$Margin\, of\, error = 2.06 - 1.82 = 0.24$
The margin of error is 0.24. The sample mean is 1.82.

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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\$.

STEP 1

Assumptions
1. The confidence interval is (1.58, 2.06)
2. The confidence interval is symmetric around the sample mean

STEP 2

The confidence interval is defined as the range in which we are confident that the population mean lies. It is symmetric around the sample mean. So, the sample mean is the midpoint of the confidence interval.
$Sample\, mean = (Lower\, limit + Upper\, limit) / 2$

STEP 3

Now, plug in the given values for the lower limit and upper limit to calculate the sample mean.
$Sample\, mean = (1.58 + 2.06) / 2$

STEP 4

Calculate the sample mean.
$Sample\, mean = (1.58 + 2.06) / 2 = 1.82$

STEP 5

STEP 6

Now, plug in the given values for the upper limit and the calculated sample mean to calculate the margin of error.
$Margin\, of\, error = 2.06 - 1.82$

STEP 7

Calculate the margin of error.
$Margin\, of\, error = 2.06 - 1.82 = 0.24$
The margin of error is 0.24. The sample mean is 1.82.

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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\$.

STEP 1

Assumptions1. The confidence interval is (1.58, 2.06)2. The confidence interval is symmetric around the sample mean

STEP 2

STEP 3

Now, plug in the given values for the lower limit and upper limit to calculate the sample mean.Sample mean=(1.58+2.06)/2Sample\, mean = (1.58 + 2.06) / 2Samplemean=(1.58+2.06)/2

STEP 4

Calculate the sample mean.Sample mean=(1.58+2.06)/2=1.82Sample\, mean = (1.58 + 2.06) / 2 = 1.82Samplemean=(1.58+2.06)/2=1.82

STEP 5

STEP 6

Now, plug in the given values for the upper limit and the calculated sample mean to calculate the margin of error.Margin of error=2.06−1.82Margin\, of\, error = 2.06 - 1.82Marginoferror=2.06−1.82

STEP 7

Calculate the margin of error.Margin of error=2.06−1.82=0.24Margin\, of\, error = 2.06 - 1.82 = 0.24Marginoferror=2.06−1.82=0.24The margin of error is 0.24. The sample mean is 1.82.

Start learning now

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

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\$.

Assumptions
1. The confidence interval is (1.58, 2.06)
2. The confidence interval is symmetric around the sample mean

Now, plug in the given values for the lower limit and upper limit to calculate the sample mean.
$Sample\, mean = (1.58 + 2.06) / 2$

Calculate the sample mean.
$Sample\, mean = (1.58 + 2.06) / 2 = 1.82$

Now, plug in the given values for the upper limit and the calculated sample mean to calculate the margin of error.
$Margin\, of\, error = 2.06 - 1.82$

Calculate the margin of error.
$Margin\, of\, error = 2.06 - 1.82 = 0.24$
The margin of error is 0.24. The sample mean is 1.82.