Question 2 (20 Marks) The following is a stem-and-leaf display representing the

Question

Question 2 (20 Marks) The following is a stem-and-leaf display representing the weekly rental cost (in S) during the first quarter of 2017, for a sample of 30 tenants renting one-bedroom units in one of the Melbourne's suburbs. Summary of Descriptive Statistics Stem-and-Leaf Display X: Weekly Rental Cost Stem unit: 10 34 0 35 0 36 0000 37 00055 38 000555 39 00055 40 0055 4105 420 43 0 Mean Standard Error Median Mode Standard Deviation Sample Variance Kurtosis 384.33 3.86 385 360 21.16 447.82 2.60 0.07 90 340 430 11530 30 Range Minimum Maximum Sum Count (a) Present a table with the values summarized in the stem-and-leaf display. (5 Marks) (b) Within what range would you expect 68% of the rental cost for a one-bedroom apartment unit to lie? Justify your answer. (5 Marks) (c) Find the Z-score for a rental cost of $365. Comment on the relative position of this rental cost in relation to the sample. (5 Marks) (d) You met a tenant who paid $450 per week. Using the empirical analysis, would you expect this tenant to be renting a one-bedroom unit similar to those in the sample? (5 Marks)

Explanation / Answer

A) 340, 350, 360, 360, 360, 360, 370, 370, 370, 375, 375, 380, 380, 380, 385, 385, 385, 390, 390, 390, 395, 395, 400, 400, 405, 405, 410, 415, 420, 430

B) At 68% the critical value is Zc = 0.99

The range is

Mean +/- Zc * SD/sqrt (n )

= 384.33 +/- 0.99 * 21.16/sqrt(30)

= 384.33 +/- 3.825

= 380.505, 388.155

C) Z-score

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