Question

Do political science classes require more writing than history classes? The 57 ran- domly selected political science classes assigned an average of 14.3 pages of essay writing for the course. The standard deviation for these 57 classes was 4.7 pages. The 49 randomly selected history classes assigned an average of 12.8 pages of essay writing for the course. The standard deviation for these 49 classes was 4.1 pages. a) What is the Null and alternative hypotheses. b) What can be concluded at the a = 0.01 level of significance? c) In words what is your final conclusion.

Answer 1

a)

we have to test that political science classes need more writing classes than history so

$H_0: \mu_{political.science}=\mu_{history},H_a: \mu_{political.science}>\mu_{history}$

b)

let political science is sample 1 hence we have

sample size =n1=57 sample mean=m1=14.3 sample SD=S1=4.7

history is sample 2 hence we have

sample size =n2=49 sample mean =m2=12.8 sample SD=S2=4.1

now test statistics is given by

$Z=\frac{m1-m2}{\sqrt{\frac{S1^2}{n1}+\frac{S2^2}{n2}}}=\frac{14.3-12.8}{\sqrt{\frac{4.7^2}{57}+\frac{4.1^2}{49}}}=1.75$

(as n1,n2>30 so we can use Z statistics)

as test is right tailed so

P-Value =P(Z>1.75) =0.04

since P value is more than level of significance hence we failed to reject H0

c)

we do not have enough evidence to conlcude that political science classes need more writing than history classes.