The manager of a local specialty store is concerned with a possible slowdown in payments by her customers.She measures the rate of payment in terms of the average number of days receivables are outstanding.Generally,the store has maintained an average of 50 days with a standard deviation of 10 days.A random sample of 25 accounts gives an average of 54 days outstanding with a standard deviation of 8 days.Calculate the appropriate test statistic to test the hypotheses.
A)-2.00
B)-2.50
C)12.50
D)2.50
E)2.00

Question

Quizplus · Accepted Answer

We can use a one-sample t-test since the sample size is small (n=25) and population standard deviation is unknown. The null hypothesis is that the average number of days receivables are outstanding is still 50 days, and the alternative hypothesis is that it has increased (i.e. one-tailed test).

The test statistic can be calculated as:

t = (sample mean - population mean) / (sample standard deviation / sqrt(sample size))
t = (54 - 50) / (8 / sqrt(25))
t = 2.50

Using a t-table with 24 degrees of freedom (n-1), at a significance level of 0.05 and a one-tailed test, the critical value is 1.711. Since our calculated t-value (2.50) exceeds the critical value (1.711), we reject the null hypothesis and conclude that there is evidence of a slowdown in payments by customers.

The Manager of a Local Specialty Store Is Concerned with a Possible