A study was conducted to determine the proportion of people who dream in black and white instead of color. Among 318 people over the age of 55, 77 dream in black and white, and among 298 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. H: P, # P2 OF. Ho: P1 = P2 H: P, #P2 H: P1 P2 O E. Ho: P1 #P2 OD. Ho: P1 SP2 H: P1 + P2 H,: P1 =P2 Identify the test statistic. z= 6,52 (Round to two decimal places as needed.) Identify the P-value. P-value = 0.000 (Round to three decimal places as needed.) What is the conclusion based on the hypothesis test? the null hypothesis. There is sufficient evidence to support the claim that the proportion of people the significance level of a = 0.05, so over 55 who dream in black and white is greater than the proportion for those under 25. The P-value is less than reject b. Test the claim by constructing an appropriate confidence interval. The 90% confidence interval is< (P1-P2)

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A study was conducted to determine the proportion of people who dream in black and white instead of color. Among 318 people over the age of 55, 77 dream in black and white, and among 298 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.

Options for hypotheses:
- \( H_1: p_1 < p_2 \)
- \( H_1: p_1 > p_2 \)
- \( H_1: p_1 \neq p_2 \)
- \( O \: D. \: H_0: p_1 \leq p_2 \: \text{and} \: H_1: p_1 \neq p_2 \)
- \( O \: E. \: H_0: p_1 = p_2 \: \text{and} \: H_1: p_1 \neq p_2 \)
- \( O \: F. \: H_0: p_1 = p_2 \: \text{and} \: H_1: p_1 \neq p_2 \)

Identify the test statistic:
- \( z = 6.52 \) (Round to two decimal places as needed.)

Identify the P-value:
- \( \text{P-value} = 0.000 \) (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 \( \alpha = 0.05 \), so **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 90% confidence interval is \( \_\_\_\_ < (p_1 - p_2) < \_\_\_\_ \) (Round to three decimal places as needed.)

Enter your answer in the edit fields and then click Check Answer.
Transcribed Image Text:A study was conducted to determine the proportion of people who dream in black and white instead of color. Among 318 people over the age of 55, 77 dream in black and white, and among 298 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. Options for hypotheses: - \( H_1: p_1 < p_2 \) - \( H_1: p_1 > p_2 \) - \( H_1: p_1 \neq p_2 \) - \( O \: D. \: H_0: p_1 \leq p_2 \: \text{and} \: H_1: p_1 \neq p_2 \) - \( O \: E. \: H_0: p_1 = p_2 \: \text{and} \: H_1: p_1 \neq p_2 \) - \( O \: F. \: H_0: p_1 = p_2 \: \text{and} \: H_1: p_1 \neq p_2 \) Identify the test statistic: - \( z = 6.52 \) (Round to two decimal places as needed.) Identify the P-value: - \( \text{P-value} = 0.000 \) (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 \( \alpha = 0.05 \), so **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 90% confidence interval is \( \_\_\_\_ < (p_1 - p_2) < \_\_\_\_ \) (Round to three decimal places as needed.) Enter your answer in the edit fields and then click Check Answer.
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