Question

1. Lehman College claims that its average class size is more than 30 students in a class. A outside organization takes a sample of 40 classrooms to see how many students are in each class. The organization found that the average number of students in a class was 25, with a sample standard deviation of 16 students. The study is going to use an alpha of .05 for their critical values. Please answer the following questions. (points: 10)
   1. What is the null and alternative hypotheses for the question? Please write out the hypotheses below. (2)
   2. Which distribution do we use and why?
   3. What is the critical value for this distribution? (1)
   4. What is the value of the Statistic for the sample? Show work (2)
   5. Do we reject the null hypothesis? Please write the hypotheses in the context of the problem. (3)

Answer 1

Solution :

= 30

=25

S =16

n = 40

This is the right tailed test .

The null and alternative hypothesis is ,

H0 :    = 30

Ha : >30

Test statistic = t

= ( - ) / S / n

= (25-30) / 16 / 40

= −1.976

Test statistic = t =−1.976  

P-value =0.9724

= 0.05  

P-value ≥

0.9724 ≥ 0.05

Fail to reject the null hypothesis .

There is insufficient evidence to suggest that