Question

A certain small town has a population of 5000 residents. You want to calculate a confidence interval for the average number of gallons of gas bought per month by the residents of this town. You want to be 95% confident that the true value of the population mean is within your interval, and you need to have a margin of error no higher than 10 gallons per month. Based on your previous research in similar towns, you believe that the population standard deviation is 50 gallons per month. Give the appropriate statistical symbol or formula for each of the following numbers in this problem: 1. 5000 = 2. 50 = 3. 95% = 4. What is the value of a? 5. What is the value of a/2 ? 6. What is the value of a 2? 7. What will be the width of your confidence interval from the smaller number to the larger number? (Hint: Think about how the MOE is related to the width of the confidence interval.) 8. Which of the following statements is the correct way to make a general statement about the confidence interval? a. We are 95% confident that is in the intervall - to +0. b. We are 95% confident that is in the interval - top +. c. We are 95% confident that is in the interval - tox+ . d. We are 95% confident that is in the interval - tox+B. e. We are 2.5% confident that is in the interval - 10 10 X+0. f. We are 5% confident that is in the interval - tof+ . 9. How many residents of the town do you need to include in your sample in order to develop a confidence interval of the appropriate width and the appropriate confidence level? 10. You also need to this confidence interval in the big city is also so our confidence 10. You also need to create a confidence interval for gasoline consumption for a big city with 1,000,000 residents. This confidence interval must have a width of 20 and a 95% confidence level. The estimated population standard deviation in the big city is also 50 gallons per month. How many residents of the big city do you need to sample in order to create your confidence interval?

please answer questions 7,9,10

Answer 1

7) Width of the interval = 2 * MOE

= 2 * 10

= 20

9) At 95% confidence level, the critical value is z_0.025 = 1.96

Margin of error = 10

or, z_0.025 * $\sigma/\sqrt n$ = 10

or, 1.96 * 50/$\sqrt n$ = 10

or, n = (1.96 * 50/10)^2

or, n = 97

10) Margin of error = 20/2

or, z_0.025 * $\sigma/\sqrt n$ = 10

or, 1.96 * 50/$\sqrt n$ = 10

or, n = (1.96 * 50/10)^2

or, n = 97