9. A random sample of 400 US adults over the age of 65 is collected to determine
ID: 3312644 • Letter: 9
Question
9. A random sample of 400 US adults over the age of 65 is collected to determine the prevalence of colorectal cancer. In the sample, it was found that about 4.9% of the adults had colorectal cancer. Construct a 90% confidence interval for the true percent of adults over the age of 65 that have colorectal cancer. 10. Suppose a random sample of 100 Berkshire pigs resulted in a mean weight of 48 pounds. If the population standard deviation is = 3.2 pounds, construct a 90% confidence interval for the mean weight of Berkshire pigs. Give the endpoints of the interval, rounded to two decimal places and interpret your interval with a sentence.Explanation / Answer
9)
sample size i.e n = 400
sample proportion i.e p = 0.049 or 4.9%
standard deviation of true mean i.e p = [p*(1-p)/n]0.5 = [0.049*(1-0.049)/400]0.5
= 0.0108
90% confidence interval of normal distribution is (mean -1.645*sd, mean +1.645*sd)
so 90% conidence interval of true percent of adults is (0.049 - 1.645*0.0108, 0.049 + 1.645*0.0108)
i.e (0.0312, 0.0668)
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