The average gasoline prices from 110 randomly selected cities across the United States are listed below.

Question

The average gasoline prices from 110 randomly selected cities across the United States are listed below.

3.455     3.509     3.376     3.483    4.106    3.915    3.586     3.858      3.107    3.936

Test the claim that the standard deviation of gas prices across the country is $0.3. Assume normality, and use a 0.05 significance level.

1) State the null and alternative hypotheses

A)       B)   

C)      D)   

Answer A, B, C, or D in the box

Ho: 

H1: 

2) Compute test statistics. Round the answer to one decimal place.

Test statistics = 

3) Compute the critical value. Round your answer to one decimal place.

 Critical Value on the left = 

 Critical Value on the right = 

4) Decision

E) Reject the Ho

F) Do not reject the Ho

Type E or F in the box 

5) Conclusion

G) There is enough evidence to support the claim that the standard deviation of gas prices across the country is $0.3.

H) There is not enough evidence to support the claim that the standard deviation of gas prices across the country is $0.3.

Type G or H in the box 

Answer 1

1) NULL HYpothesis is standard deviation = 0.3

2)

The test statistic formula is:

ChiSquareX_2 = (N-1)* (sample_standard_deviation)^2 / (hypothetical_standard_deviation)^2

The sample standard deviation is (10-1)*(0.309153126)^2 / (0.5)^2

= 3.440723591360587536

3)

With 29 df, Chi Square table via Excel says the p-value is

ChiSq.Dist(3.440723,29,true) = 0.055762895

4)

NULL Hypothesis ACCEPTED, as 0.05 < p-value

The statistical sample supports the hypothesis that

the standard deviation is 0.3