# solution

Refer to Example 5.4. Suppose an estimate of Â is given by Â  .75

a. If the level of confidence remains 99% but the desired width of the interval is reduced to 0.3, what is the necessary sample size?

b. If the level of confidence is reduced to 95% but the desired width of the interval remains 0.5, what is the necessary sample size?

c. If the level of confidence is increased to 99.5% but the desired width of the interval remains 0.5, what is the necessary sample size?

d. Describe the impact on the value of the sample size of increases (decreases) in the level of confidence for a fixed desired width.

e. Describe the impact on the value of the sample size of increases (decreases) in the desired width for a fixed level of confidence.

Example 5.4

Refer to Exercise 5.3. Describe a process to select a sample of face masks from the manufacturer to evaluate the claim.

Exercise 5.3

Face masks used by firefighters often fail by having their lenses fall out when exposed to very high temperatures. A manufacturer of face masks claims that for its masks the average temperature at which pop-out occurs is 550Â°F. A sample of 75 masks is tested, and the average temperature at which the lenses popped out was 470Â°F. Based on this information is the manufacturerâ€™s claim valid?

a. Identify the population of interest to the firefighters in this problem.

b. Would an answer to the question posed involve estimation or hypothesis testing?

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