Question

A study was conducted to determine the proportion of people who dream in black and white instead of color. Among 312 people over the age of​ 55, 75 dream in black and​ white, and among 296 people under the age of​ 25, 16 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.) Identify the test statistic: z=_______; Identify the P-value: P-value=______

What is the conclusion based on the hypothesis test?

The P-value is ______ the significance level of alpha=0.05, so ______ the null hypothesis. There is _____ evidence to support the claim that the proportion of people over 55 who dream in black and white is greater than the proportion of those under 25.

b. Test the claim by constructing an appropriate confidence interval.

The 90% confidence interval is ____ < (p₁-p₂) < ______

What is the conclusion based on the confidence interval?

Because the confidence interval limits _____ 0, it appears that the two proportions are ________. Because the confidence interval limits include _____ values, it appears that the proportion of people over 55 who dream in black and white is ______ proportion of those under 25.  

c. What is an explanation for the results is that those over the age of 55 grew up exposed to media that was displayed in black and white. Can these results be used to verify that explanation?

Answer 1