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, 80 dream in black and white, and among 291 people under the age 25, 18 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). a. test the claim using a hypothesis test b.test the claim by constructing an appropriate confidence interval c. an explanation given for the results in that those over the age 55 grew up exposed to media that was mostly displayed in black and white. can these results be used to verify that explanation

Answer 1

Explanation:

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?Identify the test statisticZ=___ ( round to two decimal places as needed)Identify the P-Value ( round to three decimal places as needed)P=___( round to three decimal places as needed)What is the conclusion based on the hypothesis​ test?The P-value is _____(more than or less than) the significane level of a=0.01 so _____( reject or fail to reject) the null hypothesis. There is____(sufficient or insufficient) 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)<____ ( how do you find the confidence interval?)( round to three decimal places as needed)What is the conclusion based on the confidence​ interval?Because the confidence interval limits ______( do not include or do include) 0, it appears that the two proportions are ___(equal or not equal). Becasue the confidence interval limits include ____(only positive or only negative) values, it appears that the proportion of people over 55 who dream in black and white is ____less than or greater than the proportion for those under 25c. 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. 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.b. Yes. The results can be used to verify the given explanation because the difference in proportions is practically significant.c. Yes. The results can be used to verify the given explanation because the difference in proportions is statistically significant.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 cannot be used to verify the cause of such a difference.