Question

A study was conducted to determine the proportion of people who dream in black and white instead of color. Among 317 people over the age of 55, 79 dream in black and white, and among 310 people under the age of 25, 10 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. Complete parts (a) through (c) below: a. Ho: P1 = P2 Ha: P1 > P2 b. Ho: P1 = P2 Ha: P1 ≠ P2 c. Ho: P1 ≠ P2 Ha: P1 = P2 Identify the test statistic. z = (Round to two decimal places as needed) Identify the P-value. P-value (Round to three decimal places as needed.) What is the conclusion based on the hypothesis test? The P-value is less than the significance level of a = 0.01, reject the null hypothesis. 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. b. Test the claim by constructing an appropriate confidence interval. The 98% confidence interval is (P1 - P2) (Round to three decimal places as needed) What is the conclusion based on the confidence interval? Because the confidence interval limits do not include 0, it appears that the two proportions are significantly different. The proportion of people over 55 who dream in black and white is greater than the proportion for those under 25. c. 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? A. Yes. The results can be used to verify the given explanation because the difference in proportions is practically significant. B. Yes. The results can be used to verify the given explanation because the difference in proportions is statistically significant. C. No. The results speak to a possible difference between the proportions of people over 55 and under 25 who dream in black and white, but the results cannot be used to verify the cause of such a difference. D. No. The results speak to a possible difference between the proportions of people over 55 and under 25 who dream in black and white.

A study was conducted to determine the proportion of people who dream in black and white instead of color. Among 317 people over the age of 55, 79 dream in black and white, and among 310 people under the age of 25, 10 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. Complete parts (a) through (c) below:

a. Ho: P1 = P2
Ha: P1 > P2

b. Ho: P1 = P2
Ha: P1 ≠ P2

c. Ho: P1 ≠ P2
Ha: P1 = P2

Identify the test statistic.

z = (Round to two decimal places as needed)

Identify the P-value.

P-value (Round to three decimal places as needed.)

What is the conclusion based on the hypothesis test?

The P-value is less than the significance level of a = 0.01, reject the null hypothesis. 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.

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

The 98% confidence interval is (P1 - P2) (Round to three decimal places as needed)

What is the conclusion based on the confidence interval?

Because the confidence interval limits do not include 0, it appears that the two proportions are significantly different. The proportion of people over 55 who dream in black and white is greater than the proportion for those under 25.

c. 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?

A. Yes. The results can be used to verify the given explanation because the difference in proportions is practically significant.
B. Yes. The results can be used to verify the given explanation because the difference in proportions is statistically significant.
C. No. The results speak to a possible difference between the proportions of people over 55 and under 25 who dream in black and white, but the results cannot be used to verify the cause of such a difference.
D. No. The results speak to a possible difference between the proportions of people over 55 and under 25 who dream in black and white.

Added by Tamara J.

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