Question

The class sizes of elementary school classes in a public school district are normally distributed with an unknown population mean and standard deviation. A random sample of 27 classes is taken and results in a sample mean of 20 students and sample standard deviation of 6 students. The margin of error for a 98% confidence interval estimate for the population mean using the Student's t-distribution is 2.86. Find a 98% confidence interval estimate for the population mean using the Student's t-distribution.

Answer 1

Answer: $(17.14,\ 22.86)$

Step-by-step explanation:

The confidence interval estimate for the population mean is given by :-

$\overline{x}\pm ME$, where $\overline{x}$ is the sample mean and ME  is the margin of error.

Given : Sample mean: $\overline{x}=20$

The margin of error for a 98% confidence interval estimate for the population mean using the Student's t-distribution : $ME=2.86$

Now, the confidence interval estimate for the population mean will be :-

$20\pm2.86=(20-2.86,\ 20+2.86)=(17.14,\ 22.86)$

Hence, the 98% confidence interval estimate for the population mean using the Student's t-distribution =  $(17.14,\ 22.86)$