## Question

A gym consultant want to study if single people go to gym more often than married people. He surveyed 8 single people and 6 married people using the following questionnaire, where a score for each answer are given alongside the answer.

• How often do you go to gym?

Less than once a week 1 once a week 2

2~3 times a week 3

4~6 times a week 4

More than 6 times a week 5

The answers from the 14 people are recorded in Excel file A2.xlsx. Use the data to answer the following questions.

1. Compute the rank sum of the group of single respondents and the rank sum of the married respondents.

2. From the data, can you conclude that single people go to gym more often than married people at the 5% level? Write down the 5 steps of hypothesis testing.

A consultant wants to study the factors that affect the expected wage and help his three clients to decide what their expected wage should be given their personal attributes. The personal attributes of the three clients are presented in Table 1. The consultant obtains a dataset of 526 individuals that has their monthly wage in thousands (wage), years of education (educ), years of experiences (exper), their gender (female, a dummy that equals one if the individual is female) and marriage status (marriage, a dummy that equal one if the individual is married). Use the data in Wage.xlsx and Table 1 to answer question B, C, and D.

Table 1: Personal attributes of three clients

educ exper Gender Marriage

Abby 9 12 Female Married

Ben 16 0 Male Unmarried

Cindy 20 5 Female Unmarried

Question B (5 marks)

Estimate the regression model:

wage = β0 + β1female + ϵ

using the data in Wage.xlsx.

1. All other factors being equal, is there evidence that men have higher wage than women? Test the claim at the 5% significance level. Write down the 5 steps of the test.

2. What assumptions need to satisfy to conduct valid hypothesis test in question B2? Do you think these assumptions are satisfied in the model specified in Equation 1 ? Briefly explain.

Question C (9 marks)

Estimate the multiple linear regression model:

wage = β0 + β1educ + β2exper + β3female + ϵ

using the data in Wage.xlsx.

1. Write down the fitted model.

2. Interpret the estimated coefficients.

3. All other factors being equal, is there evidence that men have higher wage than women? Test the claim at the 5% significance level. Write down the 5 steps of the test.

4. Is your conclusion from question C3 different from question B1? If so, briefly explain why.

5. Compute the expected wage for your three clients in Table 1 using model (2) and the estimated parameters.

6. If your client Ben decides to get 4 more years of education by going into a PhD program, how would his expected salary change?

Question D (5 marks)

The consultant suspects that marriage would affect the wage of female and the wage of male differently. Build a model that allows him to estimate the wage differential between married male and married female and the wage differential between single male and single female.

1. Write down the model you would suggest the consultant to use.

2. What is the estimated wage differential between married male and married female?

3. What is the estimated wage differential between single male and single female?

4. From the results, do marriage affect the wage of female and male differently?

## Solution Preview

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Question ARank Sum of Single = 30

Rank sum of married = 17

Null Hypothesis : H0 : single people go to gym less or equal often than married people

Alternative Hypothesis: single people go to gym more often than married people

Level of significance = 5%

Test statistic T = WB = 17 because nB < nA

Decision rule: If T = WB >= Tu

Since Tl = 32 and Tu = 58

Since 17 < 58, therefore we will accept the null and conclude that there is no enough evidence that : single people go to gym more often than married people

Question B

Null hypothesis : H0...

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