Question

In: Statistics and Probability

You have just been promoted to supervisor of a department that maintains records for billing. The...

You have just been promoted to supervisor of a department that maintains records for billing. The mean number of records that was made under the old supervisor was 27 within one hour with a standard deviation of 8. This was adopted as the standard for the population of entries. You need to make the case to your boss that your changes have improved the number that can be entered in one hour. You take a survey of 40 of your employees and find a mean of 29 records entered within one hour. Test your claim at the .05 level of significance. Be sure to show your hypothesis. What do you conclude? Would your results change if you used a .10 significance level? Do you have evidence for your boss that you have improved the process?

Solutions

Expert Solution

H0: Null Hypothesis: = 27

HA: Alternative Hypothesis: > 27

SE = /

= 8/

= 1.2649

Test Statistic is given by:

Z = (29 - 27)/1.2649

= 1.5811

= 0.05

From Table, critical value of Z = 1.645

Since the calculated value of Z = 1.5811 is less than critical value of Z = 1.645, the difference is not significant. Fail to reject null hypothesis.

Conclusion:
The data do not support the claim that your changes have improved the number that can be entered in one hour.

= 0.10

From Table, critical value of Z = 1.28

Since the calculated value of Z = 1.5811 is greater than critical value of Z = 1.28, the difference is significant. Reject null hypothesis.

Conclusion:
The data support the claim that your changes have improved the number that can be entered in one hour.

Your results would change if you used a .10 significance level. You have evidence for your boss that you have improved the process.

orchestra answered 1 year ago
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