A company produces two types of smartphones, A and B. The company wants to compare the mean battery life of the two types of smartphones. The battery life is normally distributed with unknown population standard deviations. The company selects a random sample of 25 smartphones of each type and measures their battery life in hours. The sample means and sample standard deviations are as follows:

Type A: x?A = 40 hours, sA = 5 hours
Type B: x?B = 45 hours, sB = 4 hours

a) State the null and alternative hypotheses for testing the difference in means between the two types of smartphones.

b) Calculate the pooled estimate of the population variance assuming equal variances.

c) Calculate the test statistic for testing the difference in means between the two types of smartphones using a 5% significance level.

d) Determine the critical value for the test statistic and state the decision rule.

e) Make a decision regarding the null hypothesis and interpret the result.

f) Calculate the 99% confidence interval for the difference in means between the two types of smartphones.

g) Interpret the meaning of the confidence interval in the context of the problem.

h) Determine the sample size required for each type of smartphone if the company wants to estimate the difference in means with a 99% confidence interval that has a margin of error of 2 hours.