Question

Use the data for two Sydney suburbs to answer questions 1-5:

1. Using Excel or other appropriate software, produce two separate histograms for the median rental prices of the two selected suburbs, respectively. Use an appropriate number of bins for your histogram and remember to label the axes. Describe and compare the two histograms, including the central location, dispersion and skewness. [1 mark]

2. Compute the sample means and sample standard deviations of the median rental prices of the two selected suburbs, respectively. No need to show computational steps. [1 mark]

It is claimed that the median rental price for a two-bedroom property in Sydney is $511 per week. To investigate the claim formally, you carry out a hypothesis test – by (1) constructing a confidence interval and:

In particular, the following are two questions you want to examine:

1. whether the average rent in Suburb 1 (or Suburb 2) is equal to $511 per week
2. whether the average rent in one of the suburbs is significantly higher than the other

3. Set up the null and alternative hypotheses. Define the notation(s) clearly. [2 marks]

4. Using StatKey or other appropriate software, produce a dot plot of the bootstrap distribution (with at least 5,000 bootstrap samples) of the appropriate sample statistic for b)

Comment on its shape (e.g., central location, degree of symmetry). [1 mark]

5. With reference to the bootstrap distribution in question 4, construct two 95% bootstrap confidence intervals, one using the percentile method and another one based on normal distributions. What can you conclude at a 5% significance level? [1 mark]

Two Suburbs

Bankstown	Ryde
530	390
400	410
500	370
420	390
460	420
430	650
430	380
400	400
520	380
530	380
390	570
320	400
450	380
420	400
480	380
370	330
425	700
380	620
350	575
400	635
460	400
410	400
440	420
330	440
450	620
415	420
450	595
480	800
410	850
500	400
480	760
500	800
400	520
360	630
420	415
370	560
450	400
375	465
370	600
420	400
420	680
400	400
380	360
315	600
450	420
380	540
420	630
500	570
380	610
360	750

Answer 1

From the histogram od these Suburbs, the central location of the Bankstown is smaller than the Ryde. Similarly, the dispersion of Ryde is more than Bankstown. The Bankstown has symmetric skew whereas the Ryde has asymmetric with a positive skew.

Variable	N	Mean	StDev
Bankstown	50	422	53.26
Ryde	50	512.3	140

The mean and standard deviation of Bankstown has smaller in value compare with Ryde.

We can accept the claim that the median rental price for a two-bedroom property in Sydney is $511 per week because the 95% CI does not include that value zero.

Q. Whether the average rent in Suburb 1 (or Suburb 2) is equal to $511 per week

The p-value is less than 0.05. Hence, we reject the claim that the average rent in Suburb 1 (or Suburb 2) is equal to $511 per week

Q Whether the average rent in one of the suburbs is significantly higher than the other.

Ans:

The p-value is less than 0.05 level of significance. Hence, the average rent in one of the suburbs is significantly higher than the other.