Question

A revenue department is under orders to reduce the time small business owners spend filling out pension form ABC-5500. Previously the average time spent on the form was 67 hours. In order to test whether the time to fill out the form has been reduced, a sample of 81 small business owners who annually complete the form was randomly chosen and their completion times recorded. The mean completion time for the sample was 66.7 hours with a standard deviation of 15 hours. Conduct the test using

Answer 1

Solution:

The null and alternative hypotheses are:

Under the null hypothesis, the test statistic is:

  

  

Now the p-value is:

The p-value can be found using the below excel function:

=TDIST(0.18,80,1)

Where:

0.18 is the absolute value of the test statistic

80 is the degrees of freedom

1 stand for the one-tailed test.

Conclusion: Since the p-value is greater than the significance level, we, therefore, fail to reject the null hypothesis and conclude that there is not sufficient evidence to support the claim that time to fill out the form has been reduced.