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

DATAS FOR THE QUESTIONS ARE GIVEN ON THE ATTACHED DOCUMENT FILE

1)     A marketing consultant was in the process of studying the perceptions of married

couples concerning their monthly clothing expenditures. He believed that the

husband's perception would be higher than the wife's. To judge his belief, he takes a

random sample of ten married couples and asks each spouse to estimate the family

clothing expenditure (in dollars) during the previous month. The data are shown

 (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.

2)      The "Financier" job agency claims that graduates majoring in finance can obtain an

average of at least 40 (in $1000s) starting salary. Being a dedicated student of statistics,

you determine to test their claim, and taking a random sample of 41 graduates

majoring in finance.

The "Mathematier" job agency claims that the average starting salary of mathematics

graduates is different from that of the finance graduates. You take a random sample

of 41 graduates majoring in mathematics.

Their starting salaries are recorded in Q2.xlsx.

(a) [3 marks] Calculate the descriptive statistics of the starting salaries

(separately for the finance and mathematics graduates) using Excel.

Comment on the mean and variance of these two variables.

(b) [4 marks] Using the results from part (a), test by hand at the 10%

significance level whether the data support the assumption of equal

population variances between the starting salary of the finance graduates

and mathematics graduates.

(c) [7 marks] Assuming equal variances of these two populations, perform a

test by hand to examine the "Mathematier" job agency's claim, using a

significance level of 10%. Use Excel to confirm your test results and attach

your Excel output table.

(d) [3 marks] Given the results of your test in (ii), answer the following question

without performing any further calculations: Would the value 0 be found

within a 90% confidence interval for the true mean difference in starting

salary between finance graduates and mathematics graduates? Explain

your answer.

Question 3 [10 marks]

The general manager of a chain of hardware stores believes that experience is the most

important factor in determining the level of success of a salesperson. To examine this

belief she records last month's sales (in $1,000s) and the years of experience of 10

randomly selected sales

 (a) [5 marks] Calculate the sample correlation coefficient between years of

experience and sales (provide formulas and your calculations). Interpret

your result.

(b) [5 marks] Form a linear regression model for the two variables

????????=βo + β1 ???????? + ϵi

where ???????? are the observations of sales, and ???????? are the observations of years

of experience. Estimate the parameters (intercept and slope) for the model

(provide formulas and your calculations) and interpret the two coefficients

estimated.