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In a survey, 30 random customers who purchased concessions at a movie theater listed the money they spent. The standard deviation was found to be $1.28. Find the critical value(s) needed to test a claim that the standard deviation of all individual money spent at the concession stand at movie theaters is equal to $1.45. Use a 0.05 significance level.
a. 16.047
b. 17.708, 42.557
c. 17.708
d. 16.047, 45.722

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Work Shown:

= sigma = population standard deviation

The hypotheses are

We have a two tailed test as indicated by the alternative hypothesis. So there will be 2 chi-square critical values.

We want to find values of A and B such that

note how is the confidence level.

The two tails combine to form alpha = 0.05, so half of that is alpha/2 = 0.05/2 = 0.025

Each tail has an area of 0.025

The chi-square distribution is NOT symmetric, so we cannot use tricks earlier done with the normal distribution.

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Use a chi-square table to find the area to the right of 45.722 is roughly 0.025, so , therefore B = 45.722 approximately.

The degrees of freedom are df = n-1 = 30-1 = 29.

With the same degrees of freedom, use the table to find that which shows that A = 16.047 approximately.

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updates to

The two critical values are 16.047 and 45.722

answer:   14

step-by-step explanation:          

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