Question

Calculating Confidence Intervals

5. You have decided to find a new one-bedroom apartment to live in. You want to find an apartment no further than a 30 miles from EKU. Using Zillow you take a random sample of 61 apartments. The mean rent of the sample is 640 dollars and the standard deviation 55 dollars. You want to use 95% confidence interval for the mean monthly rent for one-bedroom apartments within 30 miles of EKU to get an idea of how much on average people spend. Confirm that the sample size is large enough, calculate a 95% confidence interval and interpret the interval. (Round your answer to 2 decimal places)

6. Using the information in question 5 calculate a 95% interval assuming you sampled 10 apartments instead of 30. You do not need to check the sample size or interpret the interval. (Round your answer to 2 decimal places

7. Using the information in question 5 calculate a 95% interval assuming you sampled 101 apartments instead of 30. You do not need to check the sample size or interpret the interval. (Round your answer to 2 decimal places)

8. Compare your answers from questions 5-7. What happens to a confidence interval when the sample size changes but everything else remains the same?

Answer 1

5)

x?= 640

sigma= 55

n= 61

alpha=0.05 then Z(alpha/2)= 1.96

Margin of error E=Z(alpha/2)*sigma/sqrt(n)=13.80237566

95% Confidence interval for population mean =(x?-E,x?+E)

rounded lower bound= 626.1976

rounded upper bound= 653.8024

6)

x?= 640

sigma= 55

n= 10

alpha=0.05 then Z(alpha/2)= 1.96

Margin of error E=Z(alpha/2)*sigma/sqrt(n)=34.08935318

95% Confidence interval for population mean =(x?-E,x?+E)

rounded lower bound= 605.9106

rounded upper bound= 674.0894

7)

x?= 640

sigma= 55

n= 101

alpha=0.05 then Z(alpha/2)= 1.96

Margin of error E= Z(alpha/2)*sigma/sqrt(n)= 10.72650091

95% Confidence interval for population mean =(x?-E,x?+E)

lower bound= 629.2734991

upper bound= 650.7265009

rounded lower bound= 629.2735

rounded upper bound= 650.7265

8)

As the sample size increases confidence interval become wider and when we talk smaller sample size it become narrow.

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