A simple random sample of items resulted in a sample mean of . The population standard deviation is . a. Compute the confidence interval for the population mean. Round your answers to one decimal place. ( , ) b. Assume that the same sample mean was obtained from a sample of items. Provide a confidence interval for the population mean. Round your answers to two decimal places. ( , ) c. What is the effect of a larger sample size on the interval estimate? Larger sample provides a - Select your answer - margin of error.

(a): The 95% confidence interval is (46.4, 53.6)

(b): The 95% confidence interval is (47.9, 52.1)

(c): Larger sample gives a smaller margin of error.

Step-by-step explanation:

Given

-- sample size

-- sample mean

--- sample standard deviation

Solving (a): The confidence interval of the population mean

Calculate the standard error

The 95% confidence interval for the z value is:

Calculate margin of error (E)

The confidence bound is:

--- approximated

--- approximated

So, the 95% confidence interval is (46.4, 53.6)

Solving (b): The confidence interval of the population mean if mean = 90

First, calculate the standard error of the mean

The 95% confidence interval for the z value is:

Calculate margin of error (E)

The confidence bound is:

--- approximated

--- approximated

So, the 95% confidence interval is (47.9, 52.1)

Solving (c): Effect of larger sample size on margin of error

In (a), we have:

In (b), we have:

Notice that the margin of error decreases when the sample size increases.

a.

step-by-step explanation:

step 1 distribute 2 to every term in the parentheses

step 2 add 10 on both sides of the equal sign