Question

The author of an introductory textbook on business statistics completed a study using 30 undergraduate statistics students selected at random from a large university. The students were given a comprehensive test that took them an average of 90 minutes to complete with a sample standard deviation of 15 minutes. Construct and interpret the 90% confidence interval for the population mean time it would take for all statistics students at the university to complete this test.

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 90

sample standard deviation = s = 15

sample size = n = 30

Degrees of freedom = df = n - 1 = 30-1=29

At 90% confidence level the t is ,

= 1 - 90% = 1 - 0.9 = 0.1

/ 2 = 0.1/ 2 = 0.05

t /2,df = t0.05,29 = 1.699

Margin of error = E = t/2,df * (s /n)

= 1.699 * (15 / 30)

E = 4.7

The 90% confidence interval estimate of the population mean is,

- E < < + E

90 - 4.7 < < 90 + 4.7

85.3< < 94.7

(85.3,94.7)

First we find the degrees of freedom,then find t value.then find margin of Error by formula t/2,df * (s /n) then answer is 4.7.then we find confidence interval of 90% by formula - E < < + E then answer is  85.3< < 94.7,