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Question: Two local post offices are interested in knowing the average number of Christmas cards that are mailed out from the towns that they serve. A random sample of 80 households from Town A showed that they mailed an average of 28.55 Christmas cards with a standard deviation of 10.30. The corresponding values of the mean and standard deviation produced by a random sample of 58 households from Town B were 33.67 and 8.97 Christmas cards. Assume that the distributions of the numbers of Christmas cards mailed by all households from both these towns have the same population standard deviation.
a. Construct a 95% confidence interval for the difference in the average numbers of Christmas cards mailed by all households in these two towns.
b. Using the 10% significance level, can you conclude that the average number of Christmas cards mailed out by all households in Town A is different from the corresponding average for Town B?
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