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 for0

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?

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, the true mean amount of time these batteries will last.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? Roundupto the nearest whole number.