Question

A study was conducted to determine the proportion of people who dream in black and white instead of color. Among 288 people over the age of​ 55, 68 dream in black and​ white, and among 297 people under the age of​ 25, 15 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. Identify the p value? Test the claim by constructing an appropriate confidence level? What is the conclusion base on the hypothesis test? What is the conclusion base on the confidence level?

Answer 1

H0 : p1 =p2
Ha: p1 > p2

test statistics:

p1 = 68/288 = 0.236
p2 = 15/297 = 0.051

pcap = (68 + 15)/(288 + 297) = 0.1419

z = (p1 - p2)/sqrt(pcap*(1-pcap)/ *(1/n1+ 1/n2))
= (0.236 - 0.051) /sqrt(0.1419 *(1-0.1419) *(1/288+1/297))
= 6.41

p value = 0.0001

Reject H0 as p value < 0.05

z value at 95% = 1.96

CI = (p1 - p2) +/- z *sqrt(p1*(1-p1)/n1 + p2*(1-p2)/n2_
= (0.236 - 0.051) +/- 1.96 *sqrt(0.236*(1-0.236)/288 + 0.051*(1-0.051)/297)
= (0.1133 , 0.2579 )

As the confidence interval does not contain hypothesised value 0 So, reject H0