Question

Hypothesis Test:

A study was conducted to determine the proportion of people who dream in black and white instead of color. Among 310 people over the age of​ 55, 80 dream in black and​ white, and among 306 people under the age of​ 25, 19 dream in black and white. Use a 0.01 significance level to test the claim that the proportion of people over 55 who dream in black and white is greater than the proportion for those under 25.

Answer 1

P1 :- The proportion of people over the age of​ 55 who dream in black and white instead of color.

P2 :- The proportion of people over the age of​ 25 who dream in black and white instead of color.

To Test :-

H0 :- P1   P2

H1 :- P1 > P2

Test Statistic :-

is the pooled estimate of the proportion P
= ( x1 + x2) / ( n1 + n2)
= ( 80 + 19 ) / ( 310 + 306 )
= 0.1607

Z = 6.62

Test Criteria :-
Reject null hypothesis if

= 6.62 > 2.33, hence we reject the null hypothesis
Conclusion :- We Reject H0

There is sufficient evidence to support the claim that the proportion of people over 55 who dream in black and white is greater than the proportion for those under 25 at 1% level of significance.