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Chapter 9: Problem 97

Two years ago, \(75 \%\) of the customers of a bank said that they were satisfied with the services provided by the bank. The manager of the bank wants to know if this percentage of satisfied customers has changed since then. She assigns this responsibility to you. Briefly explain how you would conduct such a test.

Short Answer

Expert verified
The steps are to formulate the hypotheses, set a significance level and choose the test statistic, collect and analyze a sample, and draw a conclusion based on the analysis.

Step by step solution

01

Formulate Hypotheses

The null hypothesis (H0) would be: The percentage of satisfied customers is still 75%. The alternative hypothesis (H1) would be: The percentage of satisfied customers is different than 75%.
02

Choose Significance Level and Test Statistic

Choose a significance level, often 5%, that you will use to reject the null hypothesis. The test statistic in this case would be the sample proportion, as we're testing a certain proportion.
03

Collect and Analyze Sample

Collect data by conducting a new survey for the current customers of the bank to know about their satisfaction. Analyze the results either by calculating confidence intervals or by using a Z test, since we're working with a large sample.
04

Draw a Conclusion

After analyzing the data, decide whether there is enough evidence to reject the null hypothesis. If there is, conclude that there has been a significant change in the customer satisfaction percentage. If there isn't enough evidence, conclude that there's not enough evidence to say that the proportion of satisfied customers has changed since two years ago.

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Most popular questions from this chapter

The customers at a bank complained about long lines and the time they had to spend waiting for service. It is known that the customers at this bank had to wait 8 minutes, on average, before being served. The management made some changes to reduce the waiting time for its customers. A sample of 60 customers taken after these changes were made produced a mean waiting time of \(7.5\) minutes with a standard deviation of \(2.1\) minutes. Using this sample mean, the bank manager displayed a huge banner inside the bank mentioning that the mean waiting time for customers has been reduced by new changes. Do you think the bank manager's claim is justifiable? Use the \(2.5 \%\) significance level to answer this question. Use both approaches.

A study claims that \(65 \%\) of students at all colleges and universities hold off-campus (part-time or full-time) jobs. You want to check if the percentage of students at your school who hold off-campus jobs is different from \(65 \%\). Briefly explain how you would conduct such a test. Collect data from 40 students at your school on whether or not they hold off-campus jobs. Then, calculate the proportion of students in this sample who hold off-campus jobs. Using this information, test the hypothesis. Select your own significance level.

The manager of a restaurant in a large city claims that waiters working in all restaurants in his city earn an average of \(\$ 150\) or more in tips per week. A random sample of 25 waiters selected from restaurants of this city yielded a mean of \(\$ 139\) in tips per week with a standard deviation of \(\$ 28\). Assume that the weekly tips for all waiters in this city have a normal distribution. a. Using the \(1 \%\) significance level, can you conclude that the manager's claim is true? Use both approaches. b. What is the Type I error in this exercise? Explain. What is the probability of making such an error?

Dartmouth Distribution Warehouse makes deliveries of a large number of products to its customers. To keep its customers happy and satisfied, the company's policy is to deliver on time at least \(90 \%\) of all the orders it receives from its customers. The quality control inspector at the company quite often takes samples of orders delivered and checks to see whether this policy is maintained. A recent sample of 90 orders taken by this inspector showed that 75 of them were delivered on time. a. Using the \(2 \%\) significance level, can you conclude that the company's policy is maintained? b. What will your decision be in part a if the probability of making a Type \(I\) error is zero? Explain.

Explain when a sample is large enough to use the normal distribution to make a test of hypothesis about the population proportion.
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