Question

7. If I have a population of an unknown mean and unknown standard deviation, what is the 95% confidence interval estimate of the mean if a. A random sample of size 25 gives a mean of 50 and a standard deviation of 12 b. A random sample of size 16 gives a mean of 50 and a standard deviation of 12

8. The average cost per night of a hotel room in New York City is $325. Assume this estimate is based on a sample of 100 hotels and that the sample standard deviation is $75. a. What is the 95% confidence interval estimate of the population mean? b. What is the 99% confidence interval estimate of the population mean?

9. If I have a sample of 200 randomly selected people in a city of whom 120 are Christians, what would be a 95% confidence interval for the proportion of Christians in that city? If I want my confidence interval with a margin of error of 1% or less, how many people should I have in my sample? PLEASE DO THIS IN EXCEL AND SHOW FORMULA

Answer 1

7)

Mean = 50
Sample size (n) = 25
Standard deviation (s) = 12
Confidence interval(in %) = 95

Since we know that

Required confidence interval =
Required confidence interval = (50.0-4.104, 50.0+4.104)
Required confidence interval = (45.896, 54.104)

b) Mean = 50
Sample size (n) = 16
Standard deviation (s) = 12
Confidence interval(in %) = 95

Since we know that
Required confidence interval =
Required confidence interval = (50.0-5.25, 50.0+5.25)
Required confidence interval = (44.75, 55.25)