1. A battery company claims that its batteries last an average of 100 hours under normal use. After several complaints that the batteries do not last this long, an independent testing laboratory decided to test the company's claim with a random sample of 42 batteries. The data from the 42 batteries appeared to be unimodal and symmetric with a mean 97 hours and a standard deviation of 12 hours. Is this evidence that the company's claim is false and these batteries actually last less than 100 hours?

Perform the test using a significance level of 0.10 (= 0.10).

What is the P-value and your decision for H₀.

2. Recall the hypothesis test done in Question 1:

A battery company claims that its batteries last an average of 100 hours under normal use. After several complaints that the batteries do not last this long, an independent testing laboratory decided to test the company's claim with a random sample of 42 batteries. The data from the 42 batteries appeared to be unimodal and symmetric with a mean 97 hours and a standard deviation of 12 hours. Is this evidence that the company's claim is false and these batteries actually last less than 100 hours?

What would be a Type I Error in the context of this problem?

The battery company's claim is actually false, but the testing lab believes these batteries last less than 100 hours on average.

The battery company's claim is actually true, but the testing lab believes these batteries last less than 100 hours on average.

The battery company's claim is actually false, but the testing lab believes these batteries last an average of 100 hours.

The battery company's claim is actually true, but the testing lab believes these batteries last an average of 100 hours.

3. A battery company claims that its batteries last an average of 100 hours under normal use. After several complaints that the batteries do not last this long, an independent testing laboratory decided to test the company's claim with a random sample of 42 batteries. The data from the 42 batteries appeared to be unimodal and symmetric with a mean 97 hours and a standard deviation of 12 hours.

Find a 90 % confidence interval for μ_μ. Round your interval values out

4. A battery company claims that its batteries last an average of 100 hours under normal use. After several complaints that the batteries do not last this long, an independent testing laboratory decided to test the company's claim with a random sample of 42 batteries. The data from the 42 batteries appeared to be unimodal and symmetric with a mean 97 hours and a standard deviation of 12 hours.

What sample size would allow us to increase our confidence level to 95% while reducing the margin of error to only 3 hours? Round up to the nearest whole number.