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Chapter 9: Q T9.11 (page 616)

1 A software company is trying to decide whether to produce an upgrade of one of its programs. Customers would have to pay \(100 for the upgrade. For the upgrade to be profitable, the company must sell it to more than 20% of their customers. You contact a random sample of 60 customers and find that 16 would be willing to pay \)100 for the upgrade.

a. Do the sample data give convincing evidence that more than 20% of the company鈥檚 customers are willing to purchase the upgrade? Carry out an appropriate test at the 伪=0.05significance level.

b. Which would be a more serious mistake in this setting鈥攁 Type I error or a Type II error? Justify your answer.

c. Suppose that 30% of the company鈥檚 customers would be willing to pay $100 for the upgrade. The power of the test to detect this fact is0.60. Interpret this value.

Short Answer

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Part (a)

Part (b)

Part (c)

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01

Part (a) Step 1:Given informaion

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Most popular questions from this chapter

Tests and confidence intervals The P-value for a two-sided test of the null hypothesis H0:渭=10is0.06

a. Does the 95% confidence interval for 渭 include 10? Why or why not?

b. Does the 90% confidence interval for 渭 include 10? Why or why not?

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Upscale restaurant You are thinking about opening a restaurant and are searching for a good location. From the research you have done, you know that the mean income of those living near the restaurant must be over \(85,000to support the type of upscale restaurant you wish to open. You decide to take a simple random sample of 50people living near one potential site. Based on the mean income of this sample, you will perform a test at the

伪=0.05 significance level of H0:渭=\)85,000versus Ha:渭>\(85,000, where 渭 is the true mean income in the population of people who live near the restaurant. The power of the test to detect that 渭=\)86,000is 0.64 Interpret this value.

Heavy bread? The mean weight of loaves of bread produced at the bakery where you work is supposed to be 1pound. You are the supervisor of quality control at the bakery, and you are concerned that new employees are producing loaves that are too light. Suppose you weigh an SRS of bread loaves and find that the mean weight is 0.975pound.

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Clean water The Environmental Protection Agency (EPA) has determined that safe

drinking water should contain at most 1.3mg/liter of copper, on average. A water supply company is testing water from a new source and collects water in small bottles at each of30randomly selected locations. The company performs a test at the 伪=0.05 significance level ofH0:渭=1.3versus Ha:渭>1.3, where 渭 is the

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a. Describe a Type I error and a Type II error in this setting.

b. Which type of error is more serious in this case? Justify your answer.

c. Based on your answer to part (b), do you agree with the company鈥檚 choice of 伪=0.05? Why or why not?
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