A study was conducted to determine the proportion of people who dream in black and white instead of color. Among 302 people over the age of 55, 62 dream in black and white, and among 306 people under the age of 25, 10 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) below.
B. Identify the test statistic
Z=___
C. Identify the P-value.
P-value=___
D. What is the conclusion based on the hypothesis test?
The P-value is (greater than/less than) the significance level of α=0.01,so (reject/ fail to reject) the null hypothesis. There is (suffiecient/ 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.
Test the claim by constructing an appropriate confidence interval.
The 90% confidence interval is ___<( p1-p2)<___
E. Because the confidence interval limits (do not include/include) 0, it appears that the two proportions are (equal/not equal) Because the confidence interval limits include (only negative/ only positive/ negative and positive) values, it appears that the proportion of people over 55 who dream in black and white is (greater than/less than/ not significantly different from) the proportion for those under 25.
F. 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?
- Yes. The results can be used to verify the given explanation or No. The results speak to a possible difference between the proportions.
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