A cell phone manufacturer claims that batteries in its latest model provide 20 hours of continuous use. In order to verify this claim, an independent testing firm checks battery life of 100 phones. They find out that the batteries in these 100 phones last an average of 19 hours with standard deviation of five hours.
a. Does this provide sufficient evidence that true mean battery life is significantly less than 20 hours? Conduct the appropriate test of hypotheses. Be sure to describe your null and alternative hypothesis, test statistic, P-value, and conclusion.
b. Illustrate type I error, type II error, and power in context of this problem.
c. Develop a 90% CI for the true average number of hours of battery life for new phone
d. Would the interval be larger or smaller if the company constructed 80% confidence interval? Discuss briefly.
e. Would the interval be larger or smaller if the company employed a sample of 200 phones instead of 100? Discuss briefly.