Question

Testing for Rank Correlation. In Exercises 7-12, use the rank correlation coefficient to test for a correlation between the two variables. Use a significance level of α = 0.05 9. Pizza and the Subway The "pizza connection" is the principle that the price of a slice of pizza in New York City is always about the same as the subway fare. Use the data listed below to determine whether there is a correlation between the cost of a slice of pizza and the subway fare. 1960 1973 1986 1995 2002 2003 2009 2013 2015 0.15 0.35 1.00 1.25 1.75 2.00 2.252.30 2.75 Year Pizza Cost 0 Subway Fare 0.15 0.35 1.00 1.35 1.50 2.00 2.25 2.50 2.7 30.2 48.3 112.3 162.2 191.9 197.8 214.5 233.0 237.2 CPI

Answer 1

From the information, observe that the pizza connection is the principle that the price of a slice of pizza in New York City is always about the same as the subway fare.

Consider Null and Alternative hypotheses.

Null hypothesis H0: There is no correlation between the cost of a slice of pizza and the subway fare.

Alternative hypothesis Ha: There is a correlation between the cost of a slice of pizza and the subway fare.

The level of significance is 0.05

Use Excel to perform Kruskal-Walls test as follows:

Step 1: insert the data into the spreadsheet.

Step 2: select the add-lns menu in the menu bar and then select the MegaStat option, after that select the Non-Parametric tests option and then select the spearmen's rank correlation coefficient test then a dialog box will open.

Step 3: Enter the data range in the input range column and click on OK.

The Excel output as follows:

Spearman Coefficient of Rank Correlation:

	Pizza cost	Subway fare
Pizza cost	1.000
Subway fare	1.000	1.000

9 sample size

$\pm$ 0.666 critical value 0.05 (two-tail)

$\pm$ 0.798 critical value 0.01 (two-tail)

The critical value of the test statistic is 0.666

Compare the calculated value with the critical value.

Here, the calculated value exceeds the critical value then fail to reject the null hypothesis.

Hence, conclude that there is no correlation between the cost of a slice of pizza and the subway fare.