Question

The commute times for workers in a city are normally distributed with an unknown population mean and standard deviation. If a random sample of 20 workers is taken and results in a sample mean of 21 minutes and sample standard deviation of 6 minutes, find a 95% confidence interval estimate for the population mean using the Student's 1-distribution The margin of error for a 95% confidence interval estimate for the population mean using the Student's t-distribution is 2.81 . Find a 95% confidence interval estimate for the population mean using the Student's I-distribution Round the final answers to two decimal places

Answer 1

Answer:

The 95% confidence interval for population mean is (18.19, 23.81).

Step-by-step explanation:

The confidence interval for population mean using the Student's t-distribution is:

$CI=\bar x\pm t_{\alpha /2, (n-1)}\frac{s}{\sqrt{n} }$

Given:

$\bar x=21\\s=6\\n=20\\\alpha =1-0.95=0.05$

The critical value of t for α = 0.05 and degrees of freedom, (n - 1) = 19 is:

$t_{\alpha /2, (n-1)}=t_{0.05/2, 19}=2.093$

Compute the 95% confidence interval for population mean as follows:

$CI=\bar x\pm t_{\alpha /2, (n-1)}\frac{s}{\sqrt{n} }\\=21\pm2.093\times \frac{6}{\sqrt{20} }\\=21\pm2.81\\=(18.19, 23.81)$

Thus, the 95% confidence interval for population mean is (18.19, 23.81).