Question

Pizza and the Subway The “pizza connection” is the principle that 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 significant linear correlation between the cost of a slice of pizza and the subway fare.

Year	1960	1973	1986	1995	2002	2003	2009	2013	2015
Pizza cost	0.15	0.35	1.00	1.25	1.75	2.00	2.25	2.30	2.75
Subway Fare	0.15	0.35	1.00	1.35	1.50	2.00	2.25	2.50	2.75
CPI	30.2	48.3	112.3	162.2	191.9	197.8	214.5	233.0	237.2

Answer 1

	Pizza cost(x)	Subway Fare(y)	xy	x2	y2
	0.15	0.15	0.0225	0.0225	0.0225
	0.35	0.35	0.1225	0.1225	0.1225
	1	1	1	1	1
	1.25	1.35	1.6875	1.5625	1.8225
	1.75	1.5	2.625	3.0625	2.25
	2	2	4	4	4
	2.25	2.25	5.0625	5.0625	5.0625
	2.3	2.5	5.75	5.29	6.25
	2.75	2.75	7.5625	7.5625	7.5625
sum	13.8	13.85	27.8325	27.685	28.0925

The formula for correlation coefficient is

Hypothesis for the Test:

• Null Hypothesis: H0: ρ = 0
• Alternate Hypothesis: Ha: ρ ≠ 0

Meaning of Hypothesis:

• Null Hypothesis H0: The population correlation coefficient IS NOT significantly different from zero. There IS NOT a significant linear relationship (correlation) between pizza cost and subway fare in the population.
• Alternate Hypothesis Ha: The population correlation coefficient IS significantly different from zero. There IS a significant linear relationship (correlation) between pizza cost and subway fare in the population.

Critical value:

n = 9

Degrees of freedom = n -2 = 9 -2 = 7

Take

This is the case for two tails test.

From the t-table the critical value is

And

The formula for the test statistic is

Since the calculated t-value is in the tailed, so we reject the null hypothesis that there is no linear relationship between the two variables.

Therefore, we can cconclude that there is a significant linear relationship (correlation) between pizza cost and subway fare in the population.