Question

A manufacturer of flashlights wants to know how well one of their newer styles is selling in a chain of large home-improvement stores. They select a simple random sample of 20 stores, record how many of the flashlights were sold in a 30-day period, and construct a 95% confidence interval for the mean number of flashlights sold. Required: a. Discuss whether this study meets the necessary conditions for constructing a confidence interval. If you think one of the conditions has not been met, what additional information would be required or what change in the study would you recommend? b. If, instead of constructing a 95% confidence interval, the flashlight manufacturer constructed a 98% confidence interval, would the 98% interval be wider, narrower, or the same width as the 95% interval? Explain. c. How would the width of confidence interval change if the flashlight manufacturer took a larger sample? Explain.

Answer 1

A. This study that the manufacturer is carrying out meets the necessary conditions for constructing a C.I.

The conditions for a confidence interval in a random sample.

• It is random given that it is a simple random sample
• It is independent given that it can be assumed that 20 is less than 10 percent of the chain of stores.
• 20<30

b. Changing from a 95 percent CI to 98% C.I would make it more possible for us to capture the value so this means it would be wider.

c. A larger sample is going to make $\frac{s}{\sqrt{n} }$ to be smaller. This is due to the fact that the value we are dividing with has become larger. So the sample would get to be narrower.

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