Question

You have a data set with a Gas Price variable. It lists the price of a gallon of regular gasoline at a randomly selected 100 gas stations around the country in a particular week. You calculate a 95% confidence interval for the mean of Gas Price, and it turns out to be $2.43 plus or minus $0.16. Which of the following most closely reflects what you can conclude? a. If your sample size had been 400, and you had observed the same sample mean but a sample standard deviation twice as large as in your original sample, the 95% confidence interval would have been approximately $2.43 plus or minus $0.08. b. If your sample size had been 400 and you had obtained the same sample mean and sample standard deviation as in your original sample, the 95% confidence interval would have been approximately $2.43 plus or minus $0.08. c. If you had observed the same sample mean and sample size, but a sample standard deviation twice as large as the one you observed, the 95% confidence interval would have been approximately $2.43 plus or minus $0.24. d. If you had observed the same sample mean and sample size, but a sample standard deviation half as large as the one you observed, the 95% confidence interval would have been approximately $2.43 plus or minus $0.04.

Answer 1

Formula for standard error is

The new sample size will be 4 times of old sample size so new standard error will be half of old standard error.

(a)

We have

That is new margin of error will be  

ME = 0.16

Hence, it is false.

(b)

We have

That is new margin of error if sample standard deviation, s, remains same will be  

Hence, it is true.

(c)

It is false.

(d)

It is false.