Question

Answer the following questions using the NYC2br.MTW file. 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.

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

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.

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

Answer 1

ANSWER:

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.

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