Question

A Walton College of Business graduate, wants to start a hot dog stand on Dickson Street. He needs to raise $15,000 for start-up supplies and equipment. He believes that in order to be successful, he would need to sell more than 300 hot dogs on average per night. He creates a survey and stands on Dickson Street asking people to state whether or not they would buy a hot dog. He notices that the demand increases significantly after midnight. Sixty people complete his survey and based on their feedback, he purchases the supplies and equipment. He opened his stand and after the first two weeks he wants to analyze his sales. He is open 5 days a week and finds the average number of hot dogs sold is 335 with a standard deviation of 50. Is he meeting his original goal to be successful? Assume a 5% level of significance for this question. "The critical value is" _________?

Answer 1

Yes, he is meeting his original goal to be successful.

The critical value is 1.833

Explanation:

H0: mu = 300

Ha: mu > 300

The test is a one-tailed test because the alternate hypothesis is expressed using greater than.

Test statistic (t) = (sample mean - population mean) ÷ (sample sd/√n)

sample mean = 335

population mean = 300

sample sd = 50

n = 2×5 = 10

t = (335 - 300) ÷ (50/√10) = 35 ÷ 15.81 = 2.21

Degree of freedom = n-1 = 10-1 = 9

Significance level = 5%

Critical value corresponding to 9 degrees of freedom and 5% significance level is 1.833.

Conclusion:

Reject the null hypothesis because the test statistic 2.21 is greater than the critical value 1.833.

His original goal to be successful is contained in the alternate hypothesis, therefore, he is meeting it.