Question

A marketing manager claims that the average 18-25 year old watches Netflix less than 26 hours per week. She collects data on 25 individuals' in the age range and interviews them about their Netflix habits. She finds that the mean number of hours that the sample spent watching Netflix was 22.4 hours. If the population standard deviation is known to be eight hours, can we conclude at the 1% significance level that she is right? State the null and alternative hypotheses. Compute the value of the test statistic. Compute the p-value. Interpret the results.

Answer 1

To Test :-

H0 :- µ ≥ 26
H1 :- µ < 26

Test Statistic :-
Z = ( X - µ ) / ( σ / √(n))
Z = ( 22.4 - 26 ) / ( 8 / √( 25 ))
Z = -2.25

Decision based on P value
Reject null hypothesis if P value < α = 0.01 level of significance
P value = P ( Z < 2.25 ) = 0.0122
Since 0.0122 > 0.01, hence we reject null hypothesis
Result :- We fail to reject null hypothesis

There is not sufficient evidence to support the claim that the average 18-25 year old watches Netflix less than 26 hours per week.