Question

a study was conducted to determine the proportion of people who dream in black and white instead of color. among 288 people over the age of 55, 64 dream in black and white, and among 299 people under the age of 25, 11 dream in black and white. use a 0.05 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. complete parts (a) through (c).
a. test the claim using a hypothesis test
consider the first sample to be the sample of people over the age of 55 and the second sample to be the sample of people under the age of 25. what are the null and alternative hypotheses for the hypothesis test?
a. ( h_0: p_1
eq p_2 ) ( h_1: p_1 = p_2 )

b. ( h_0: p_1 = p_2 ) ( h_1: p_1
eq p_2 )

c. ( h_0: p_1 leq p_2 ) ( h_1: p_1
eq p_2 )

d. ( h_0: p_1 geq p_2 ) ( h_1: p_1
eq p_2 )

e. ( h_0: p_1 = p_2 ) ( h_1: p_1 > p_2 )

f. ( h_0: p_1 = p_2 ) ( h_1: p_1 < p_2 )
identify the test statistic.
( z = ) (round to two decimal places as needed.)

Explanation:

The claim is that the proportion of people over 55 ( \( p_1 \)) who dream in black and white is greater than the proportion for those under 25 ( \( p_2 \)). The null hypothesis (\( H_0 \)) is a statement of no difference or equality, and the alternative hypothesis (\( H_1 \)) reflects the claim. So \( H_0: p_1 = p_2 \) and \( H_1: p_1 > p_2 \), which matches option E.

Answer:

E. \( H_0: p_1 = p_2 \), \( H_1: p_1 > p_2 \)