Problem
Points: 0 of 1 A 2003 study of drearning found that out of a random sample of 127 people, 85 reported dreaming in color. However, the rate of reported dreaming in color that was established in the 1940 s was 0.28 . Check to see whether the conditions for using a one-proportion z-test are met assuming the researcher wanted to test to see if the proportion dreaming in color had changed since the 1940 s. Are the conditions met? A. Yes, all the conditions are met. B. No, the observations are not independent. C. No, the sample size is not large enough to produce at least 10 successes and 10 failures. D. No, the population is not more than 10 times bigger than the sample size.
Solution
Step 1 ：Check if the observations are independent: Assuming the sample of 127 people is randomly selected, each person's response is independent of others.
Step 2 ：Check the sample size condition: There must be at least 10 successes and 10 failures. With 85 people reporting dreaming in color, there are \(127 - 85 = 42\) people not dreaming in color. Both numbers are greater than 10.
Step 3 ：Check the population size condition: Although the total population size is not given, we can assume it is significantly larger than the sample size of 127 since we are comparing to a rate from the 1940s.
Step 4 ：Since all conditions are met, the final answer is \(\boxed{A}\)
