In 2014, a group of students was interested in investigatingprices of rental accommodation in suburbs of Brisbane that areclose to the CBD and collected information on a total of 200randomly chosen dwellings in four inner western suburbs. A subsetof this data, relating to rental apartments in these suburbs isincluded below. The variables are:
Per week: weekly rental price for the apartment($);
Bedrooms: number of bedrooms in theapartment;
Sqm: size of the apartment (m2)
Furnished: whether the apartment was furnishedor not (yes/no).
The values are;
265,2,59,No
305,2,70,No
300,1,72,No
320,3,66,No
340,2,113,Yes
330,2,58,Yes
355,2,63,No
345,2,57,Yes
355,2,61,No
360,2,114,Yes
355,2,75,Yes
360,2,68,No
365,2,64,No
370,1,69,No
390,2,73,Yes
380,2,85,Yes
390,2,56,Yes
370,2,56,Yes
385,2,59,Yes
380,2,65,Yes
385,2,62,Yes
400,2,65,No
415,2,69,Yes
400,3,63,No
405,3,70,No
420,2,77,No
435,2,84,Yes
435,2,83,Yes
455,2,73,Yes
450,2,72,Yes
485,2,68,No
500,2,76,Yes
535,2,97,No
290,1,60,No
305,1,63,Yes
330,2,65,No
310,2,70,No
335,2,64,No
330,2,62,No
345,2,79,No
355,1,81,No
340,2,66,No
345,1,60,No
345,2,64,No
355,2,73,No
385,2,61,No
380,2,78,No
405,2,81,No
410,2,76,Yes
430,2,80,No
440,2,61,No
450,3,86,No
485,3,91,No
500,1,87,No
545,1,97,Yes
345,3,86,No
400,2,72,No
400,2,74,No
480,2,73,Yes
755,3,87,No
760,3,77,No
770,3,113,No
824,2,109,No
860,3,104,No
295,1,70,No
290,1,54,No
295,1,61,No
325,1,61,No
340,2,56,No
355,2,61,No
365,2,95,No
420,1,75,No
420,2,66,No
440,2,74,No
480,3,72,No
465,3,87,No
470,1,87,Yes
490,1,81,Yes
495,2,76,No
505,2,97,No
530,2,77,No
545,2,97,No
560,2,79,No
550,2,78,No
560,3,75,No
565,1,96,Yes
580,2,85,Yes
605,3,84,No
605,2,93,Yes
610,2,78,Yes
620,2,87,No
665,2,88,No
700,2,80,No
750,3,97,Yes
740,3,124,No
805,3,101,No
860,3,98,No
960,3,123,Yes
990,3,102,Yes
1195,3,133,No
1190,3,137,No
1405,3,148,Yes
1490,3,154,No
Question 3)
The students were interested in the proportion of rentalapartments in these suburbs that were leased as furnishedapartments, and whether this varied with the number of bedrooms inthese apartments. To investigate further whether the proportions offurnished apartments differ between apartments with differentnumbers of bedrooms, it is useful to test formally whether thenumber of bedrooms in an apartment and whether it is furnished ornot are independent.
a) Test whether the number of bedrooms in an apartment andwhether it is furnished or not is independent.
b) State the null hypothesis, the relevant form of the teststatistic and the approximate distribution of the test statisticfor carrying out this text.
c) Perform a hypothesis test with using α = 0.05, of whether theproportions of furnished apartments vary across number of bedrooms,that is, whether the furnishing status of an apartment isindependent of the number of bedrooms in the apartment.
Include the Following:
i) The table of expected frequencies
ii) The observed value of the test statistic
iii) The relevant degrees of freedom for the distribution of thetest statistic
IV) The resulting p-value for the test, or a rejectionregion
Conclude the test by interpreting the p-value (or rejectionregion and your observed test statistic) in terms of the originalquestion discussed above
Pls do this question with R code !!!!
