Martys Burger Barn typically maintains relatively stable sal

Marty’s Burger Barn typically maintains relatively stable sales. However, Marty has recently noticed some inconsistency in his daily sales totals. Historical sales data indicate that the standard deviation of daily sales should be $250. Marty has asked for your help in evaluating the situation, so you have correctly formulated the following hypothesis test.

H₀: sigma <= 250

H₁: sigma > 250

You have informed Marty that you intend to use a level of significance of 0.05 and that you wish to detect a true standard deviation of 500 with a power of 88%.

(a)        Identify the key assumption that is required to proceed with the test. You may make this assumption for the remainder of the problem.

(b)       Identify the appropriate sample size for the test. You may assume that this sample size is used for the remainder of the problem.

(e)        If the true standard deviation of daily sales is $250, then what is the probability you will conclude that s > 250?

(f)        If the true standard deviation of daily sales is $375, then what is the probability you will conclude that s > 250?

(g)        After collecting and analyzing appropriate data, you determine that the sample standard deviation is $317.50. Compute the test statistic.

(h)       Use the critical region to determine the conclusion of the test.

(i)        Construct the confidence interval on the standard deviation of daily sales that is most relevant to this problem.

Solution

a) that is not normal distributed and sigma is unknown

b)

sample size = 500

e) 0.05

f) 1-0.88 = 0.12