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Research Method For Business: The Fighting Fit Gymnasium has recently carried out a survey in which members who visited the Gymnasium during a particular week were asked to complete and return a questionnaire. The questions are reproduced overleaf.
Read the data into the Stata statistics software package, and answer the following questions.
1. Is there any evidence of an association between occupational status and the number of visits to the Gymnasium during the past four weeks? Carry out an appropriate hypothesis test.
2. Is there any evidence that the average customer satisfaction score is age-dependent? Carry out an appropriate hypothesis test.
3. The Gymnasium management have calculated that a monthly membership fee of at least £75 will be required to cover the investment and running costs of the upgraded Gymnasium. Test the null hypothesis that the mean willingness-to-pay for membership of the upgraded Gymnasium is at least £75, against the one-sided alternative hypothesis that the mean willingness to pay is less than £75.
4. Test whether there is any evidence of a difference between the willingness-to-pay for membership of the upgraded Gymnasium of male and female customers.
5. Estimate a two-variable linear regression to describe the relationship between household weekly net income and willingness-to-pay for membership of the upgraded Gymnasium. According to this regression, what is the estimated willingness-to-pay of a customer with a household weekly net income of £300?
6. Estimate a multiple regression in which willingness-to-pay for membership of the upgraded Gymnasium is explained by the following characteristics: gender (male/female), occupational status, and household weekly net income.
(i) Comment on the significance of each of these characteristics as determinants of willingness-to-pay.
(ii) Comment briefly on the comparison between the multiple regression estimated in Q6 and the two-variable linear regression estimated in Q5.
(iii) What is the estimated willingness-to-pay of a male self-employed customer with a household weekly net income of £500?
(iv) What is the estimated willingness-to-pay of a female employed customer with a household weekly net income of £400?
You are required to produce a brief written report containing the solutions to each of the questions. Your Stata output may be presented as an appendix, but Stata output presented without any accompanying report will be awarded a zero mark. Stata output can be used to obtain the results of all statistical tests: these do not need to be calculated manually. Please note you MUST report solutions based on your own personalised questionnaire data. Solutions based on another student’s data will be awarded a zero mark.
FIGHTING FIT GYMNASIUM – CUSTOMER SURVEY QUESTIONNAIRE
Q1 State whether male or female:
Male Female
Q2 State your age group
16-24 25-44 45-64 65+
Q3 State your occupational status:
Employed
Self-employed
Student
Unemployed
Out of the workforce (e.g. retired, not seeking employment)
Q4 What is your household weekly net income?
Q5 During the past four weeks, how many times have you visited Fighting Fit Gymnasium?
Number of visits: 1-3 4-6 7-10 11-15 More than 15
Q6 Fighting Fit Gymnasium is considering investing in a major upgrade of its facilties. The current monthly membership fee is £50. What is the maximum amount you would be willing to pay for monthly membership to the upgraded Gymnasium?
Q7 On a scale of 5 to 1, what is your overall level of satisfaction with the services provided by Fighting Fit Gymnasium?
Highly satisfied 5 4 3 2 1 Highly dissatisfied
The responses are coded as follows:
Q1: Male=0, Female=1
Q2: 16-24=1; 25-44=2; 45-64=3; 65+=4
Q3: Employed=1; Self-employed=2; Student=3; Unemployed=4; Out of workforce=5
Q4: Monetary amount (continuous data)
Q5: 1-3 visits = 1; 4-6 = 2; 7-10 = 3; 11-15 = 4; More than 15 = 5
Q6: Monetary amount (continuous data)
Q7: Highly satisfied = 5, …, Highly dissatisfied = 1
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