Question

An experiment compares the taste of instant coffee with fresh-brewed coffee. Each subject tastes two unmarked cups of coffee, one of each type, in random order and states which he or she prefers. Of the 60 subjects who participate in the study, 25 prefer instant coffee and the other 35 prefer fresh-brewed. Take p to be the proportion of the population that prefers fresh-brewed coffee.

Test the claim that a majority of coffee drinkers prefer the taste of fresh-brewed coffee, using 5% significance.

Define hypotheses. (a) HA: p 6= 0.5833 H0: p = 0.5833 (b) HA: p > 0.5833 H0: p ≤ 0.5833 (c) HA: p > 0.50 H0: p ≤ 0.50 (d) HA: p 6= 0.50 H0: p = 0.50 (e) HA: p > 0 H0: p ≤ 0

Answer 1

To Test :-

H0 :- P = 0.50
H1 :- P > 0.50

P = X / n = 35/60 = 0.5833

Test Statistic :-
Z = ( P - P0 ) / √ ((P0 * q0)/n))
Z = ( 0.583333 - 0.5 ) / √(( 0.5 * 0.5) /60))
Z = 1.29

Test Criteria :-
Reject null hypothesis if Z > Z(α)
Z(α) = Z(0.05) = 1.645
Z < Z(α) = 1.291 < 1.645, hence we fail to reject the null hypothesis
Conclusion :- We Fail to Reject H0

Decision based on P value
P value = P ( Z > 1.291 ) = 0.0984
Reject null hypothesis if P value < α = 0.05
Since P value = 0.0984 > 0.05, hence we fail to reject the null hypothesis
Conclusion :- We Fail to Reject H0

There is insufficient evidence to support the claim that majority of coffee drinkers prefer the taste of fresh-brewed coffee.