Question

A manager was assigned the task of investigating the error in payments for routine purchases made by the purchasing department. The manager randomly selected 12 payments, investigated them thoroughly, and determined the payment error for each of these payments. The payment error was defined as the difference between the amount paid and what should have been paid. The payment errors determined for these selected payments were as follows: $17 $25 $14 -$10 $20 $40 $35 $30 $28 $22 $15 $16 a. What is the 95% confidence interval for the population mean payment error? b. Suppose a recent company report inferred that the mean payment error may be running as high as $25. That led the manager to test the null hypothesis that the population mean payment error is equal to $25 versus the alternative that the population mean payment error is not equal to $25. Using a level of significance equal to 0.01, perform this hypothesis test . c. Suppose another manager used this same data to test the null hypothesis that the population mean payment error is less than or equal to $15 versus the alternative that the population mean payment error is greater than $15. What is the test statistic for this hypothesis testing situation? What is the critical value at a level of significance equal to 0.01? What is the conclusion

Answer 1

Solution: a. What is the 95% confidence interval for the population mean payment error?

Answer: The 95% confidence interval for the population mean payment error is:

Where:

is the sample mean and is:

is the sample standard deviation and is:

is the sample size and is:

is the critical value at 0.05 significance level for and is:

Therefore, the 95% confidence interval is:

Therefore the 95% confidence interval for the population mean payment error is:

b. Suppose a recent company report inferred that the mean payment error may be running as high as $25. That led the manager to test the null hypothesis that the population mean payment error is equal to $25 versus the alternative that the population mean payment error is not equal to $25. Using a level of significance equal to 0.01, perform this hypothesis test

Answer: The null and alternative hypotheses under consideration are:

Under null hypothesis, the test statistic is:

  

  

Therefore, the test statistic is:

Now, the two tailed critical value at 0.01 significance level for is:

Since the statistic is less than the critical value, we therefore fail to reject the null hypothesis and conclude that the mean payment error is equal to $25.

c. Suppose another manager used this same data to test the null hypothesis that the population mean payment error is less than or equal to $15 versus the alternative that the population mean payment error is greater than $15. What is the test statistic for this hypothesis testing situation? What is the critical value at a level of significance equal to 0.01? What is the conclusion

Answer:

Answer: The null and alternative hypotheses under consideration are:

Under null hypothesis, the test statistic is:

  

  

Therefore, the test statistic is:

Now, the right tailed critical value at 0.01 significance level for is:

Since the statistic is less than the critical value, we therefore fail to reject the null hypothesis and conclude that the mean payment error is less than or equal to $15.