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 37 workers is taken and results in a sample mean of 31 minutes and sample standard deviation of 5 minutes.

Use Excel to find a 95% confidence interval estimate for the population mean using the Student's t-distribution.

Round the final answers to two decimal places.

Answer 1

Solution, Given that, x = 31 S = 5 n = 37 c = 95% = 0.95 At 95 % confidence interval t is x = -c=1-0.950.05 0.05 2 = 0.025 d.f. -n-1-37-1 = 36 t - 2.028 Z table t /2. dif. 0.025, 36 Margin of essor E - (using dif. (e t H2 - 2.028 5 √37 = 1.667 95% confidence internal mean is XtE X-E < u u <x+E 31-1.667 Lu <31+ 1.667 29.333 < u < 32.667 ( 29.33 ,32.67)