Question

Shell Oil Company produces natural gas, gasoline, oil, and other chemical products. A manager of the credit card department for the company wanted to assess the monthly balance of credit card holders. An auditor selects a random sample of 100 accounts and finds that the mean owed is $83.40 with a standard deviation of $23.65. At the 0.10 level of significance, is there evidence to suggest that the average monthly balance differs from $79.00? Using the critical value approach, determine which of the following is the correct decision?

Reject the null hypothesis.

Accept the null hypothesis.

Reject the alternative hypothesis.

Do not reject the null hypothesis.

Answer 1

We have to test Ho : = 79 Vs H1 : 79

Test statistic t = ( xbar - )/(s/√n)

t = ( 83.40 - 79)/(23.65/√100)

t = 1.86

tCritical for a = 0.10 and d.f = n -1 = 99

tCritical = t​​​​​​a/2 , n-1 = t​​​​​​0.05,99

tCritical = 1.66

Decision rule : Reject Ho if t > 1.66 otherwise we fail to reject Ho

Our t = 1.86 > 1.66

Decision : Reject the null hypothesis