Question

1. A company claims that the average lifespan of a bicycle tire that they manufacture is 1200 miles. You randomly and independently collect a sample of 31 of these tires and find that the average distance these tires lasted was 1125.7 miles, with a standard deviation of 275 miles.

A 90% confidence interval for the population mean lifetime of these tires is (1041.9, 1209.5).

Select all true statements.

a. The confidence interval indicates that the company's claim that their tires last 1200 miles is ok.

b. The confidence interval indicates that the actual life of their tires is less than 1200 miles.

c. A 95% confidence interval calculated from the same data might not contain 1200.

d. One interpretation of this interval is "I'm 90% confident that the average lifespan of these tires is between 1041.9 miles and 1209.5 miles."

e. This confidence interval indicates the average life of the company's tires is probably less than 1250 miles.

f. It's possible that these tires actually last an average of 1300 miles.

2. A company claims that the average lifespan of a bicycle tire that they manufacture is 1200 miles. You randomly and independently collect a sample of 31 of these tires and find that the average distance these tires lasted was 1125.7 miles, with a standard deviation of 275 miles. You suspect the company is overstating how long their tires last. You formulate your suspicion as a left tailed hypothesis test. Your null hypothesis is "the average lifespan of these tires is 1200 miles."

You use an alpha of 0.05 (unless otherwise stated below) and find a p-value of 0.071.

Select all true statements.

a. You reject the null hypothesis.

b. You fail to reject the null hypothesis.

c. This test shows that the average lifespan of these tires is less than 1200 miles.

d. You may have made a Type I error with your conclusion.

e. You may have made a Type II error with your conclusion.

f. If you instead used an alpha of 0.10 you would reject the null hypothesis.

Answer 1

1. Answer:

• a. The confidence interval indicates that the company's claim that their tires last 1200 miles is ok.
• d. One interpretation of this interval is "I'm 90% confident that the average lifespan of these tires is between 1041.9 miles and 1209.5 miles."
• e. This confidence interval indicates the average life of the company's tires is probably less than 1250 miles.

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2. Answer:

• b. You fail to reject the null hypothesis.
• e. You may have made a Type II error with your conclusion.
• f. If you instead used an alpha of 0.10 you would reject the null hypothesis.