Question

Question Set 2: Two Independent Means

Answer the following questions using the NYC2br.MTW file. You can find this dataset in this assignment in Canvas (i.e., where you downloaded this document and where you’ll upload your completed lab). Data were collected from a random sample of two-bedroom apartments posted on Apartments.com in Manhattan and Brooklyn.

A. What is one type of graph that could be used to compare the monthly rental rates of these two-bedroom apartments in Manhattan and Brooklyn? Explain why this is an appropriate graph. [10 points]

B. Using Minitab Express, Construct the graph you described in part A to compare the Manhattan and Brooklyn apartments in this sample. [10 points]

C. Use the five-step hypothesis testing procedure given below to determine if the mean monthly rental rates are different in the populations of all Manhattan and Brooklyn two-bedroom apartments. If assumptions are met, use a t distribution to approximate the sampling distribution. You should not need to do any hand calculations. Use Minitab Express and remember to include all relevant output. [30 points]

Step 1: Check assumptions and write hypotheses

Step 2: Calculate the test statistic

Step 3: Determine the p value

Step 4: Decide to reject or fail to reject the null hypothesis

Step 5: State a real-world conclusion

This is the data set.

Area   Rent   Address
Manhattan   5495   56 W 91st ST
Manhattan   2200   10 W 107th ST
Manhattan   3386   181 W 126th ST
Manhattan   2383   236 W 135th ST
Manhattan   2550   3 W 137th ST
Manhattan   2600   533 W 142nd ST
Manhattan   2600   260 W 171st ST
Manhattan   2150   518 W 204th ST
Manhattan   3200   680 Fort Washington AVE
Manhattan   2200   69 Cooper ST
Manhattan   2199   24 Thayer ST
Manhattan   2950   45 Tiemann PL
Manhattan   2780   510 E 117th ST
Manhattan   2695   314 E 106th ST
Manhattan   2900   320 E 93rd ST
Manhattan   5900   58 W 58th ST
Manhattan   25000   160 Central Park S
Manhattan   15000   30 E 62nd ST
Manhattan   4650   220 E 54th ST
Manhattan   2175   431 E 9th ST
Manhattan   7950   18 W 48th ST
Manhattan   2675   534 W 47th ST
Manhattan   3507   331 W 52nd ST
Manhattan   5195   236 E 47th ST
Manhattan   7750   445 W 35th ST
Manhattan   6883   1050 6th AVE
Manhattan   13754   7 W 21st ST
Manhattan   3995   172 Spring ST
Manhattan   5750   133 2nd AVE
Manhattan   6000   364 E 10 ST
Manhattan   3900   216 Centre ST
Manhattan   3400   167 Mott ST
Manhattan   16000   20 Greene ST
Manhattan   3200   174 Canal ST
Manhattan   4000   196 Stanton ST
Manhattan   8500   46 Warren ST
Manhattan   5950   108 South ST
Manhattan   3600   75 Wall ST
Manhattan   6598   44 Trinity PL
Manhattan   7995   377 Rector PL
Manhattan   6508   41 River TER
Brooklyn   3300   76 Franklin ST
Brooklyn   3150   80 Meserole ST
Brooklyn   4225   224 Wythe AVE
Brooklyn   3256   228 Manhattan AVE
Brooklyn   2500   1421 Dekalb AVE
Brooklyn   2900   381 Myrtle AVE
Brooklyn   4350   9 Old Fulton ST
Brooklyn   5500   365 Bridge ST
Brooklyn   3900   117 Congress ST
Brooklyn   2600   224 Sachett ST
Brooklyn   4358   280 Ashland PL
Brooklyn   3125   229 5th AVE
Brooklyn   3900   753 Carroll ST
Brooklyn   3450   497 Saint Marks AVE
Brooklyn   2000   544 Franklin AVE
Brooklyn   2575   237 Troy AVE
Brooklyn   2300   223 Rockaway AVE
Brooklyn   2150   231 Amboy ST
Brooklyn   2000   789 Belmont AVE
Brooklyn   1800   542 E 93rd ST
Brooklyn   4213   125 Parkside AVE
Brooklyn   12500   3 Pierrepont PT
Brooklyn   5000   135 Willow ST
Brooklyn   2500   224 22nd ST
Brooklyn   2400   2025 Dorchester RD
Brooklyn   1900   7301 4th AVE
Brooklyn   2000   2071 E 61st ST
Brooklyn   1925   1063 E 2nd ST
Brooklyn   2300   2031 W 6th ST
Brooklyn   2250   9747 Shore RD
Brooklyn   3500   155 Oceana DR
Brooklyn   2759   3510 Neptune AVE
Brooklyn   2200   2832 Bragg ST
Brooklyn   1950   1780 W 3rd ST
Brooklyn   2400   9602 4th AVE
Brooklyn   3500   26 Bay Ridge AVE
Brooklyn   2400   1519 New York AVE
Brooklyn   3304   941 Washington AVE
Brooklyn   3300   412 Herkimer ST
Brooklyn   5203   593 Baltic ST
Brooklyn   7500   78 Amity ST
Brooklyn   2625   692 Chauncey ST
Brooklyn   15000   260 Park AVE
Brooklyn   8750   100 Jay ST
Brooklyn   6455   475 Clermont AVE
Brooklyn   5775   300 Ashland PL

Answer 1

I have done all calculations in Minitab software.

A) Boxplot:

​​​​​​Average monthly rental rates in Manhattan is greater Brooklyn . Values are more diapersed in Manhattan than brooklyn. Also we get the Idea of skewness from boxplot. Homogeneity of variance can be tested in Boxplot which is essential assumption of 2 sample t test.

B) A 2-sample t-test to determine whether there is a difference in the patient ratings between the hospitals.

1. Open the sample data.

Assumption of two sample t test:

In order to test whether there is a difference between population means, we are going to make three assumptions:

The two populations have the same variance. This assumption is called the assumption of homogeneity of variance.
The populations are normally distributed.
Each value is sampled independently from each other value. This assumption requires that each subject provide only one value. If a subject provides two scores, then the scores are not independent.

1. Open the 2-Sample t dialog box.
2. PC: STATISTICS > Two Samples > t
3. From the drop-down list, select Each sample is in its own column.
4. In Samples1, enter Manhattan
5. In Sample 2, enter Brooklyn's
6. Click OK.

Interpret the results

The null hypothesis states that the difference between monthly rental rates of two bedroom apartments in Manhattan and Brooklyn is 0. Because the p-value is 0.035, which is less than the significance level of 0.05, the consultant rejects the null hypothesis and concludes that the monthly rental rates of two different populations are different.