Question

Test the claim that the mean GPA of night students is larger than 3.1 at the 0.01 significance level. The null and alternative hypothesis would be:

H 0 : p = 0.775 H 1 : p ≠ 0.775

H 0 : μ = 3.1 H 1 : μ ≠ 3.1

H 0 : μ ≥ 3.1 H 1 : μ < 3.1

H 0 : p ≤ 0.775 H 1 : p > 0.775

H 0 : μ ≤ 3.1 H 1 : μ > 3.1

H 0 : p ≥ 0.775 H 1 : p < 0.775

The test is: left-tailed or right-tailed or two-tailed

Based on a sample of 40 people, the sample mean GPA was 3.12 with a standard deviation of 0.08

The p-value is: (to 2 decimals)

Based on this we: Fail to reject the null hypothesis or Reject the null hypothesis

Answer 1

(first part) right choice is H 0 : μ ≤ 3.1 H 1 : μ > 3.1

Here we want to test the claim that the mean GPA of night students is larger than 3.1, so μ > 3.1 will be the alternate hypothesis and opposite of it μ ≤ 3.1 will be the null hypothesis,

(second part) The test is right-tailed

In  right tailed test  the alternate hypothesis statement contains a greater than (>) symbol. In other words, the inequality points to the right.

(Third part)p-value=0.06

here we use t-test as the population standard deviation is not given

statistic t=(-μ)/(s/)=(3.12-3.1)/(0.08/sqrt(40))=1.5811 with n-1=40-1=39 df

p-value=0.06 (using ms-excel=tdist(1.5811,39,1))

(this is one tailed p-value as the alternate hypothesis is right-one-tailed)

(fourth part)  Fail to reject the null hypothesis

since p-value=0.06 is more than level of significance alpha=0.01, so we : Fail to reject the null hypothesis H0( or accept null hypothesis H0)