Question

A beer distributer claims that a new display featuring a life-size picture of a well-known rock singer will increase product sales in supermarkets by an average of 50 cases in a week. For a random sample of 20 high volume liquor outlets, the average sales increase was 41.3 cases, and the population standard deviation was 12.2 cases. Test at the 10% level the null hypothesis that the population mean sales increase is at least 50 cases, stating any assumptions you make (Using the Critical-value approach and p-value approach).

Answer 1

To Test :-

H0 :- µ >= 50
H1 :- µ < 50

Test Statistic :-
Z = ( X - µ ) / ( σ / √(n))
Z = ( 41.3 - 50 ) / ( 12.2 / √( 20 ))
Z = -3.1891

Test Criteria :-
Reject null hypothesis if Z < -Z(α)
Critical value Z(α) = Z(0.1) = 1.282 ( From Z table )
Z < -Z(α) = -3.1891 < -1.282
Result :- Reject null hypothesis

Decision based on P value
Reject null hypothesis if P value < α = 0.1 level of significance
P value = P ( Z < 3.1891 ) = 0.0007 ( From Z table )
Since 0.0007 < 0.1 ,hence we reject null hypothesis
Result :- Reject null hypothesis

There is isufficient evidence to support the claim that  the null hypothesis that the population mean sales increase is at least 50 cases.