Question

Construct an 80% confidence interval to estimate the population mean using the data below. What assumptions need to be made about this population?

Data:

Sample mean =35
Sample standard deviation = 8.5
Sample size = 22
The 80% confidence interval for the population mean is from a lower limit of 32.60 to an upper limit of 37.40 (Round to two decimal places as needed.)

What assumptions need to be made about this population?

A. The population follows the normal probability distribution.

B. The population follows the Student's t-distribution.

C. The population distribution is skewed to one side.

D. The population size is larger than 30.

Answer 1

To construct an 80% confidence interval for estimating the population mean using the given data, the assumption that needs to be made about the population is that the population follows the normal probability distribution.

Step-by-step explanation:

To construct an 80% confidence interval for estimating the population mean using the given data, the assumption that needs to be made about the population is that the population follows the normal probability distribution, option A.

This assumption is necessary in order to use the Z-score formula for calculating the confidence interval.

The formula for calculating the confidence interval is:

(Sample Mean) ± (Critical Value) * (Standard Error)

Using the given data:

• Sample Mean = 35
• Sample Standard Deviation = 8.5
• Sample Size = 22

We can calculate the critical value for the 80% confidence interval using a Z-table or calculator.

With that value, we can calculate the standard error and plug in the values into the formula to obtain the confidence interval.