t- table testing

Question

Test the claim that the mean GPA of night students is smaller than 3.5 at the .10 significance level.

The test statistic is:

the critical value is:

Based on a sample of 70 people, the sample mean GPA was 3.45 with a standard deviation of 0.06The test statistic is:  (to 2 decimals)The critical value is:  (to 2 decimals)Based on this we:

fail to reject the null

reject the null

Answer 1

Null Hypothesis: mean (mu) = 3.5

Alternate Hypothesis: mean (mu) < 3.5

Degrees of Freedom is 70-1=69, so use available lower value from t-distribution table for 60 DOF and 0.1 tail value = 1.296. Since left-tail test the critical value is -1.296

xbar = sample mean

mu = population mean

sd = sample standard deviation = 0.06

n = sample size = 70

t stat = (xbar - mu)/(sd/sqrt(n)) = (3.45 - 3.5)/(0.06/sqrt(70)) = -6.97

the t-stat is < the critical value so we would reject the null hypothesis