Question

An automobile club reported that the average price of regular gasoline in a certain state was $2.61 per gallon. The following data show the price per gallon of regular gasoline for 15 randomly selected stations in the state. Complete parts a through c below.

2.64	2.72	2.53	2.65	2.57
2.69	2.62	2.51	2.65	2.63
2.56	2.51	2.66	2.62	2.65

a.	Construct a 99​% confidence interval to estimate the average price per gallon of gasoline in the state.

The 99% confidence interval to estimate the average price per gallon of gasoline in the state is from $_____to $_____

b. Do the results from this sample validate the automobile​ club's findings?

A. Since the population​ mean, ​$2.61​, is not contained within the 95​% confidence​ interval, it can be said with 95​% confidence that the sample validates the automobile​ club's findings.

B. Since the population​ mean, ​$2.61​, is contained within the 95​% confidence​ interval, it can be said with 95​% confidence that the sample validates the automobile​ club's findings.

C. Since the population​ mean, ​$2.61​, is not contained within the 95​% confidence​ interval, it can be said with 95​% confidence that the sample does not validate the automobile​ club's findings.

D. Since the population​ mean, ​$2.61​, is contained within the 95​% confidence​ interval, it can be said with 95​% confidence that the sample does not validate the automobile​ club's findings.

c. What assumptions need to be made about this​ population?

A. The only assumption needed is that the population standard deviation is known.

B. The only assumption needed is that the population distribution is approximately uniform.

C. The only assumption needed is that the population distribution is approximately normal.

D. No assumptions are required.

Answer 1

Solution:- Given that samples : 2.64,2.72,2.53,2.65,2.57,2.69,2.62,2.51,2.65,2.63,2.56,2.51,2.66,2.62,2.65

X = 2.614, s = 0.0641, n = 15, df = 14, t = 2.977

a. 99% confidence interval for the avergae price per gallon of gasonline :
X +/- t*s/sqrt(n)

= 2.614 +/- 2.977*0.0641/sqrt(15)
= (2.5647,2.6633)

b. option B.

c. option C.