Question

Use a 0.05 significance level to test the claim that male professors have higher course evaluation scores than female professors. Use the following statistics:

Male: n=53, x=4.01, s=0.53

Female: n=40, x=3.79, s=0.51

a) Write down the claim

b) Write down the null hypothesis and the alternative hypothesis. Indicate which one is the claim.

c) Draw the probability distribution curve. Write down the testing statistic and the P-Value on the graph.

d) Determine whether to reject the null hypothesis. Write the conclusion in a complete sentence.

Answer 1

Ans:

a)

Claim:

Male professors have higher course evaluation scores than female professors.

b)

H_A is claim.

c)

pooled standard deviation=SQRT(((53-1)*0.53^2+(40-1)*0.51^2)/(53+40-2))=0.5215

standard error=0.5215*sqrt((1/53)+(1/40))=0.1092

Test statistic:

t=(4.01-3.79)/0.1092

t=2.015

df=53+40-2=91

p-value=tdist(2.015,91,1)=0.0235

d)As,p-value<0.05,we reject the null hypothesis.

There is sufficient evidence to support the claim that male professors have higher course evaluation scores than female professors.