1) A marketing consultant was in the process of studying the perceptions of married couples concerning their monthly clothing expenditures.

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(a) Can the consultant conclude at the 5% significance level that the

husband's mean estimate for the family clothing expenditure is higher than 310

(dollars)?

(b) Assume that the true population mean of the husband's estimate is

315 (dollars) and the true population standard deviation is 34 (dollars).

Calculate the probability of type II error of the hypothesis test

H0: μh = 310

HA: μh > 310

with a 5% significance level.

(c) Can the consultant conclude at the 5% significance level that the

majority (more than half) of wives believe that the family clothing expenditure

is not less than 320 (dollars)?

(d) Can the consultant conclude at the 5% significance level that the

husband's mean estimate is higher than the wife's mean estimate? (Hint: you

firstly have to decide the two samples are independent or paired.)

(e) Calculate 95% confidence interval for the population mean difference

between the husband's estimate and wife's estimate, and briefly describe what

the confidence interval tells you.