Question

The student body at many community colleges is considered a “commuter population”. The following question was asked of the student affairs office at one such college; How far does the average community college student commute to college daily? The answer was no more than 9 mi. The inquirer was not convinced and decided to test the statement. She took a random sample of 20 students and found a mean community distance of 10.22 mi with the sample standard deviation 5 mi. State and test the hypothesis as a significance level of α = 0.05.

Answer 1

Solution :

Given that,

This a right (One) tailed test.

The null and alternative hypothesis is,  

Ho: 9

Ha: 9

The test statistics,

t = ( - )/ (s/)

= ( 10.22 - 9 ) / ( 5 / 20 )

= 1.091

P-value = 0.1444

The p-value is p =0.1444 > 0.05, it is concluded that the null hypothesis is fail to rejected.

Conclusion :

It is concluded that the null hypothesis Ho is fail to rejected. Therefore, there is not enough evidence to claim that The answer was no more than 9 mi. , at the 0.05 significance level.