Question

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

Answer 1

Answer:

Following are the solution to this question

Step-by-step explanation:

Please find the complete question in the attached file.

In point a:

$a=0.05 \\\\| Z(0.025)|= 1.96 \text{(check in normal table)} \\\\ 95 \% \ CI \\\\\bar x \pm \ Z \times \frac{s}{\sqrt{n}}\\\\\to 80 \pm 1.96 \times \frac{15}{\sqrt{60}} \\\\\to (76.20448, 83.79552)$

In point b:

$95 \% \ CI \ is \\\\ \bar x \pm Z \times \frac{s}{\sqrt{n}}\\\\\to 80 \pm 1.96 \times \frac {15}{\sqrt{120}}\\\\\to (77.31616, 82.68384)$

In point c:

A large sample is a smaller error margin.