Question

A conservationist wants to know if the average water level in Horseshoe Lake is less than the average water level in Swan Lake. So he takes samples of water readings and obtains the data below.

	Horseshoe Lake	Swan Lake
Mean Water Level	16.1	17.5
Sample Variance	5.2	5.4
Sample Size	35	45

Test the hypothesis at the 1 % significance level.

(A) Do not reject Ho since -2.70 is less than 2.05

(B) Do not reject Ho since the p-value is equal to .0035, which is less than .02

(C) Reject Ho since -2.70 is less than -2.05

(D) Reject Ho since -2.70 is less than -2.441

(E) Reject Ho since the p-value is equal to .0070, which is less than .02

...

I know the answer is (D) but I do not know the steps and formulas/equations that I need to use to get the answer.

Answer 1

To Test :-

H0 :-  

H1 :-  

Test Statistic :-


t = -2.7014

Test Criteria :-
Reject null hypothesis if


DF = 73


Result :- Reject Null Hypothesis

Decision based on P value
P - value = P ( t > 2.7014 ) = 0.0043
Reject null hypothesis if P value <    level of significance
P - value = 0.0043 < 0.01 ,hence we reject null hypothesis
Conclusion :- Reject null hypothesis