Question

1 A software company is trying to decide whether to produce an upgrade of one of its programs. Customers would have to pay $\backslash (100$ 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 $\backslash )100$ for the upgrade.

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

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

c. Suppose that 30% of the company’s customers would be willing to pay $\$100$ for the upgrade. The power of the test to detect this fact is$0.60.$ Interpret this value.

Short answer

Part (a)

Part (b)

Part (c)

Step-by-step solution

Part (a) Step 1:Given informaion

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