A study was conducted to determine the proportion of people who dream in black a

Question

A study was conducted to determine the proportion of people who dream in black and white instead of color. Among 314 people over the age of 55, 75 dream in black and white, and among 300 people under the age of 25, 20 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) below. 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 = P_2 h_1: p_1 p_2 E H_0: p_1 greaterthanorequalto p_2 H_1: p_1 notequalto p_2 F. H_0: p_1 lessthanorequalto p_2 H_1: p_1 notequalto p_2 Identify the test statistic. z =

Explanation / Answer

The statistical software output of this problem is:

Two sample proportion hypothesis test:
p1 : proportion of successes for population 1
p2 : proportion of successes for population 2
p1 - p2 : Difference in proportions
H0 : p1 - p2 = 0
HA : p1 - p2 > 0

Hypothesis test results:

Hence,

z = 5.90

p - value = 0

There is sufficient evidence to suppor the claim.

Difference Count1 Total1 Count2 Total2 Sample Diff. Std. Err. Z-Stat P-value p1 - p2 75 314 20 300 0.17218684 0.02919684 5.8974478 <0.0001

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