A company that produces financial accounting software wants to offer better training to its customers.The training is intended to decrease the amount of time required to do complicated accounting calculations.For seven individuals,the amount of time (in minutes)to complete a complicated calculation is determined before and after completing the new training. The value of the test statistic is _____.
A) 5
B) 23
C) 7
D) 13

Question

A company that produces financial accounting software wants to offer better training to its customers.The training is intended to decrease the amount of time required to do complicated accounting calculations.For seven individuals,the amount of time (in minutes)to complete a complicated calculation is determined before and after completing the new training.  The value of the test statistic is _____.
A) 5 
B) 23 
C) 7 
D) 13

Quizplus · Accepted Answer

The problem is describing a paired t-test, where the same individuals are measured before and after an intervention (in this case, the new training). To find the test statistic, we need to calculate the difference between the before and after measurements for each individual, then calculate the mean and standard deviation of those differences.

Using the data in the table, we can calculate:

Mean difference = (5+10+2+9+5+3+3)/7 = 4.28
Standard deviation of differences: s = 3.98

The formula for the paired t-test statistic is:

t = (mean difference - hypothesized mean difference) / (s / sqrt(n))

The hypothesized mean difference is zero (i.e. the null hypothesis is that the new training has no effect on the time required to complete the calculation). Plugging in the values, we get:

t = (4.28 - 0) / (3.98 / sqrt(7)) = 3.28

Using a t-table with 6 degrees of freedom (n-1), we can find that the probability of getting a t-value this large or larger (in either direction) is approximately 0.013. Since this probability is less than the typical significance level of 0.05, we would reject the null hypothesis and conclude that the new training has a significant effect on decreasing the time required to do complicated accounting calculations.

A Company That Produces Financial Accounting Software Wants to Offer