A study was conducted to determine the proportion of people who dream in black and white instead of color. Among317people over the age of 55,69dream in black and white, and among296people under the age of 25,15dream in black and white. Use a0.05significance 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. Identify the test statistic.z=(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 P-value isthe significance level of a = 0.05, soV the null hypothesis. There isevidence to support the claim that the proportion of people over 55 who dream in black and white is greater than theproportion for thless thanAn explanationhose 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?greater thanO A. No. Thessible 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.O B. Yes. The results can be used to verify the given explanation because the difference in proportions is practically significant.O C. Yes. The results can be used to verify the given explanation because the difference in proportions is statistically significant.O 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, but the results are not statistically significant enough to verify the cause of such a difference.

Name: A study was conducted to determine the proportion of people who dream
Uploaded: 2024-03-20T07:07:00.000Z
Channel: Bartleby
Description: A study was conducted to determine the proportion of people who dream in black and white instead of color. Among317people over the age of 55,69dream in black and white, and among296people under the age of 25,15dream in black and white. Use a0.05si

n₁= 317 x₁= 69 n₂= 296 x₂= 15 α = 0.05H₀: p₁ ≤ p₂ H₁: p₁ > p₂p^₁= x₁n₁=69317=0.22p^2= x₂n₂=15296=0.05 Pooled sample proportion, p^=x₁+x₂n₁+n₂=69+15317+296=0.14The statistic for this test is the approximation of the standard normal distribution, z=(p^₁-p^₂)-(p₁-p₂)p^(1-p^).1n₁+1n₂ =(0.22-0.05)-00.14(1-0.14)×1317+1296z=6.06 The p-value of this test is one-tailed to the right, just as it is the test. p-value < .00001 The decision rule for the p-value approach is: If the p-value ≤ α, the decision is to reject the null hypothesis. If the p-value > α, the decision is to not reject the null hypothesis. The p-value is less than the significance level α = 0.05, so reject the null hypothesis. There is sufficient evidence to support the claim that the population proportion of people over the age of 55 that dreams in black and white is greater than the population of people under the age of 25 that dreams in black and white.yes, the results can be used to verify the given explanation because the difference in proportion is statistically significant.