The students were interested in the proportion of rental apartments in these suburbs that were leased as furnished apartments and whether this varied with the number of bedrooms in these apartments: investigate further whether the proportions of furnished apartments differ be- tween apartments with different numbers of bedrooms, it is useful to test formally whether the number of bedrooms in an apartment and whether it is furnished or not are independent (a) State the null hypothesis the relevant form of the test statistic and the approximate distri- bution of the test statistic for carrying out this text (b) Provide cross-tabulation of the apartment data by these two factors (you should generate this table using R)
(c) Carry out a formal test, using a = 0.05,of whether the proportions of furnished apartments varies across number of bedrooms, that is, whether the furnishing status of an apartment independent of the number of bedrooms in the apartment You may use R to carry out these calculations, but please state the following information from this test: i. the table of expected frequencies ii. the observed value of the test statistic iii. the relevant degrees of freedom for the distribution of the test statistic iv. the resulting p-value for the test, or rejection region You should also ensure that you conclude your formal test by interpreting the p-value (or rejection region and your observed test statistic) in terms of the original question discussed above:'

The students were interested in the proportion of rental apartments in these suburbs that were leased as furnished apartments and whether this varied with the number of bedrooms in these apartments 500x + 900y + 1500z = 750,000

formal test, using a = 0.05,of whether the proportions of furnished apartments varies across number of bedrooms, that is, whether the furnishing status of an apartment independent of the number of bedrooms in the apartment You may use R to carry out these calculations, but please state the following information from this test: i. the table of expected frequencies ii. the observed value of the test statistic iii. the relevant degrees of freedom for the distribution of the test statistic iv

500x + 900y + 1500z = 750,000 - - - (1)

x + y + z = 1000 - - - - (11)

x = 200 + y + z - - - - (111)

x + 2y + 3z = 1550 - - - (1V)

I bedroom = x

2 bedroom = y

3 bedroom = z

All the condition s gjvbbs'

500x + 900y + 1500z = 750,000 - - - (1)

x + y + z = 1000 - - - - (11)

x = 200 + y + z - - - - (111)

x + 2y + 3z = 1550 - - - (1V)

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