Question

A music teacher knows from past records that 60% of students taking summer lessons play the piano. The instructor believes that this proportion may have dropped due to the popularity of wind and brass instruments. A random sample of 80 students yielded 43 piano players. Use α = .05.

Answer 1

To Test :-

H0 :- P = 0.6

H1 :- P < 0.6

n = 80
P = X / n = 0.5375

Test Statistic :-


Z = -1.14

Test Criteria :-
Reject null hypothesis if

= -1.14 > -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 < -1.14 )
P value = 0.1271
Reject null hypothesis if P value <
Since P value = 0.1271 > 0.05, hence we fail to reject the null hypothesis
Conclusion :- We Fail to Reject H0

Conclusion :- Accept Null Hypothesis

There is insufficient evidence to support the  instructor believes that the proportion may have dropped due to the popularity of wind and brass instruments at 5% level of significance.