Question

1. Suppose the Dean of our college claims that, the average GPA for all students in the college is at least 3.00, with standard deviation 0.4.  However, from a class with 25 students, we find the class average GPA is 2.80.  Can we reject the dean’s claim at significance level 0.05? (We conduct a hypothesis testing).

a).  H0: mu=3.00,          Ha:

b). Calculate test statistic, here is z-value.  

c). Find pvalue.

d).  Make your decision.

Answer 1

This is the left tailed test .

The null and alternative hypothesis is

H₀ : = 3

H_a : < 3

Test statistic = z

= ( - ) /    / n

= (2.80 - 3) / 0.4 / 25

Test statistic = -2.5

P-value = 0.0124

P-value <

Reject the null hypothesis .