Clear typed answers please Question 2 (20 Marks) The following is a stem-and-lea

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Clear typed answers please

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

SOlutonb:

Rentalcost form steam and leaf plot

430

Descriptive statistics:

Solutionb:

68% of the value lie within 1 sd of the mean

lower limit=mean-sd

upper limit=mean+sd

lower limit=384.3333-21.16167=363.1716

and upper limit=384.3333+21.16167=405.495

68% of the rental cost lies in 363.17 and 405.95

Solutionc:

z score =x-mean/sd/sqrt(n)

=365-384.33/21.16167/sqrt(30)

=-0.1667

z=-0.1667

means lies 0.1667 std deviations below mean

Solutiond:

since 68% of the rental cost lies in 363.17 and 405.95,

450 is lies outside the range

so we will not expecting this tenant to be renting one-bedroom unit similar to those in the sample.

Weeklyrentalcost 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

Descriptive statistics:

Weeklyrentalcost Mean 384.3333 Standard Error 3.863574 Median 385 Mode 360 Standard Deviation 21.16167 Sample Variance 447.8161 Kurtosis -0.24948 Skewness 0.073031 Range 90 Minimum 340 Maximum 430 Sum 11530 Count 30

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