ETB2111 - Business Data Modeling - Sporting Goods Manufacturing Company - Test Statistic - Business Assessment Answer

Assessment Task:

ETB2111: Business Data Modeling Assessment Answer

Question 1
A sporting goods manufacturing company wanted to compare the performance of four designs of golf balls in terms of the average distance travelled by balls. The company approached a professional golfer and gave him 10 balls of each design for testing. The pro was not told of the type of ball that was being hit. All 40 balls were hit in a short period of time so that the environmental conditions did not affect the performance of the balls. The distances travelled in metres by each ball are given in the
table that follows.

These data are also provided in worksheet Ass1?Q1 of file “ETB2111 Ass1?S1?2019?data.xlsx” on Moodle.

(a) Name a statistical procedure that will facilitate the company make comparison of the four designs of golf balls. Using Excel, run this procedure on the given data.

(b) On the basis of average distance travelled by golf balls of each design, which design seems to be the best in producing balls with long drives? Explain your reason.

(c) Would you consider design 2 to be better than or at least comparable to design 1? Explain the reason for your choice of the design.

(d) Can we conclude at the 5% level of significance that there is a significant difference in the average distance travelled by balls of the four designs? Your answer must include the following:

(i) Appropriate null and alternative hypotheses

(ii) The value of the test statistic used and the distribution this test statistic follows

(iii) The decision rule based on the p?value

(iv) Conclusion about the average performance of four designs of balls in terms of average distance travelled.

(e) If the answer in part (d) indicates the existence of significant differences in average distances travelled by the four types of balls, apply an appropriate test to determine which pairs of ball designs produce statistically different average distances. Use a 5% level of significance and show all details.

Question 2 
Choice?Mart offered 20% discount on all items purchased on Easter Monday. The manager of Choice? Mart is interested in finding out whether purchasing behaviour (the amount spent in a single transaction) of customers is related to their gender. He asked the checkout personnel to keep record of the gender of the customer making the payment. At the conclusion of the sales on Easter Monday, he finds the amount spent and the gender of the 150 randomly selected customers. These data are
given in worksheet Ass1?Q2 of file “ETB2111 Ass1?S1?2019?data.xlsx” on Moodle.

(a) Describe the variable type and the measurement scale of variables Gender and Amount Spent.

(b) Can we conclude at 5% level of significance that on average females spend more money in a single transaction than males? Provide all necessary details on the test(s) required to support your answer, giving reason (s) for the choice of your test.

(c) What assumptions did you make in performing test (s) in part (b)?

(d) Report the proportions of males and females who spent more than $120 during Easter Monday sales

(e) On the basis of sample evidence, can we conclude that there is no difference in the proportions of males and females who spent more than $120

Question 3 
The Big Max store manager has collected data on age and amount spent in a single transaction by 1000 of its customers. The manager wishes to determine if the amount spent in a single transaction by customers is related to their age. He has classified customers into 3 age categories of ‘Young:  30 years’, ‘Middle aged: 31 to 55 years’ and ‘Older: > 55 years’. He uses four categories for amount spent in a single transaction, and defines them as: ‘1 = Casual purchase: amount spent  $148’, ‘2 =
Small purchase: amount spent between $149 and $299’, ‘3 = Medium purchase: amount spent between $300 and $ 553’ and ‘4 = Large purchase: amount spent  $554’. The data are given in worksheet Ass1?Q3 of file “ETB2111 Ass1?S1?2019?data.xlsx” on Moodle. Use Excel to analyse data and answer the following questions.

(a) Report contingency table displaying observed frequencies from cross tabbing ‘Age’ and ‘Amount spent category’.

(b) Find the percentage of Young, Middle aged and Older customers in each amount category. Explain, if any, the pattern depicted by these percentages.

(c) Using the critical value approach, can we conclude at the 1% level of significance that the amount spent in a single transaction by customers is related to their age? Your answer must include the following.
(i) Appropriate null and alternative hypotheses
(ii) Details of the analysis leading up to the value of the test statistic, and the distribution followed by the test statistic
(iii) Decision rule
(iv) Conclusion.

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