Question

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, 79 dream in black and white, and among 314 people under the age of 25, 13 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. 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? O A. Ho: P1 = P2 HD, P2 OD. HOD, 2D2 HD*P2 B. Hop, #22 H:D, = P2 O E. Ho: D = P2 H:P, MP2 OC. HOP, = P2 H: DP2 OF. Ho Do SP2 H:*P2 Identify the test statistic. 2=1 (Round to two decimal places as needed.) Identify the P-value. P-value = 0 (Round to three decimal places as needed.) What is the conclusion based on the hypothesis test? The P-value is the significance level of a = 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 for those under 25. b. Test the claim by constructing an appropriate confidence interval. The 90% confidence interval is <(P-P2) | (Round to three decimal places as needed.) What is the conclusion based on the confidence interval? Because the confidence interval limits O, it appears that the two proportions are Because the confidence interval limits include V values, it appears that the proportion of people over 55 who dream in black and white is 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? O A. Yes. The results can be used to verify the given explanation because the difference in proportions is practically significant. O B. Yes. The results can be used to verify the given explanation because the difference in proportions is statistically significant O 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. 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.

Answer 1

null Hypothesis: Ho: P1P2 alternate Hypothesis: Ha: P1-P2 > for 0.05 level with right tailed test, critical value of z= Decision rule: reject Ho if test statistic z > 1.64 Pz=xz/nz = >55 79 Pi=xy'n = 0.2484 318 estimated prop. diff =PI-P = pooled prop p =(x4+x>)/(ny+na) 0.0414 314 0.2070 0.1456 std error Se= (01 (1-01)*(1/n1+1/2) = 0.0281 test stat z=(01-02)/Se = 7.38 Pvalue = 0.0000

a)

O E. Ho: pn = P2 HP, P2

z =7.38

p value =0.000

the p value is less than ...so reject the null,,,there is sufficient evidence,,,,,,,,,,,

bv)

90% Ci =0.163 <p1-p2 <0.251

Because the confidence interval limits does not chaithappears that the two proportions are different Because the confidence interval limits include all positive values, it appears that the proportion of people over 55 who dream in black and white is greater the proportion for those under 25.

O 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.