Math / Data & Statistics

QuestionThe 'pizza connection' is the principle that the price of a slice of pizza is always about the same as the subway fare. Use the pizza and subway cost data in the table below to determine whether there is a linear correlation between these two items. Construct a scatterplot, find the value of the linear correlation coefficient r , and find the P -value of r . Determine whether there is sufficient evidence to support a claim of linear correlation between the two variables. Based on these results, does it appear that the subway fare is always about the same as a slice of pizza? Use a significance level of $\alpha=0.05$ .
Click here for data on pizza costs and subway fares over the years.
Construct a scatterplot. Choose the correct graph below. A. B. C. D.
Determine the linear correlation coefficient. The linear correlation coefficient is $r=0.987$ . (Round to three decimal places as needed.) Determine the null and alternative hypotheses. $\begin{array}{l} H_{0}: \rho=0 \\ H_{1}: \rho \neq 0 \end{array}$ (Type integers or decimals. Do not round.) Pizza Cost and Subway Fares \begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|c|} \hline Year & 1960 & 1973 & 1986 & 1995 & 2002 & 2003 & 2009 & 2013 & 2015 & 2019 & 맘 \\ \hline Pizza Cost & 0.15 & 0.35 & 1.00 & 1.25 & 1.75 & 2.00 & 2.25 & 2.30 & 2.75 & 3.00 & \\ \hline Subway Fare & 0.15 & 0.30 & 0.95 & 1.40 & 1.50 & 2.05 & 2.25 & 2.50 & 2.75 & 2.70 & \\ \hline CPI & 29 & 43.9 & 109.7 & 152.1 & 180.0 & 184.0 & 214.5 & 233.0 & 237.0 & 252.2 & \\ \hline \end{tabular}

Studdy Solution

STEP 1

1. We have data for pizza costs and subway fares for specific years.
2. We are testing for linear correlation between pizza costs and subway fares.
3. The significance level for hypothesis testing is $\alpha = 0.05$ .

STEP 2

1. Construct a scatterplot of the data.
2. Calculate the linear correlation coefficient $r$ .
3. Formulate the null and alternative hypotheses.
4. Determine the P-value for the correlation coefficient.
5. Make a decision based on the P-value and significance level.
6. Interpret the results in the context of the problem.

STEP 3

Plot the pizza costs on the x-axis and subway fares on the y-axis for each year given. Choose the correct scatterplot from options A, B, C, or D.

STEP 4

Calculate the linear correlation coefficient $r$ . The given value is:
$r = 0.987$

STEP 5

Formulate the null and alternative hypotheses:
\begin{align} H_{0}: & \quad \rho = 0 \quad \text{(no linear correlation)} \\ H_{1}: & \quad \rho \neq 0 \quad \text{(linear correlation exists)} \end{align}

STEP 6

Determine the P-value for the calculated $r$ . Use statistical software or a correlation table to find the P-value corresponding to $r = 0.987$ with the appropriate degrees of freedom.

STEP 7

Compare the P-value to the significance level $\alpha = 0.05$ . If the P-value is less than $\alpha$ , reject the null hypothesis.

STEP 8

Interpret the results: - If the null hypothesis is rejected, there is sufficient evidence to suggest a linear correlation between pizza costs and subway fares. - If the null hypothesis is not rejected, there is not enough evidence to suggest a linear correlation.
Based on the results, determine if the subway fare is always about the same as a slice of pizza.

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Studdy Solution

STEP 1

1. We have data for pizza costs and subway fares for specific years.
2. We are testing for linear correlation between pizza costs and subway fares.
3. The significance level for hypothesis testing is $\alpha = 0.05$ .

STEP 2

STEP 3

Plot the pizza costs on the x-axis and subway fares on the y-axis for each year given. Choose the correct scatterplot from options A, B, C, or D.

STEP 4

Calculate the linear correlation coefficient $r$ . The given value is:
$r = 0.987$

STEP 5

Formulate the null and alternative hypotheses:
\begin{align} H_{0}: & \quad \rho = 0 \quad \text{(no linear correlation)} \\ H_{1}: & \quad \rho \neq 0 \quad \text{(linear correlation exists)} \end{align}

STEP 6

Determine the P-value for the calculated $r$ . Use statistical software or a correlation table to find the P-value corresponding to $r = 0.987$ with the appropriate degrees of freedom.

STEP 7

Compare the P-value to the significance level $\alpha = 0.05$ . If the P-value is less than $\alpha$ , reject the null hypothesis.

STEP 8

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Studdy Solution

STEP 1

1. We have data for pizza costs and subway fares for specific years.2. We are testing for linear correlation between pizza costs and subway fares.3. The significance level for hypothesis testing is α=0.05\alpha = 0.05α=0.05.

STEP 2

STEP 3

Plot the pizza costs on the x-axis and subway fares on the y-axis for each year given. Choose the correct scatterplot from options A, B, C, or D.

STEP 4

Calculate the linear correlation coefficient rrr. The given value is:r=0.987 r = 0.987 r=0.987

STEP 5

Formulate the null and alternative hypotheses:\begin{align*} H_{0}: & \quad \rho = 0 \quad \text{(no linear correlation)} \\ H_{1}: & \quad \rho \neq 0 \quad \text{(linear correlation exists)} \end{align*}

STEP 6

Determine the P-value for the calculated rrr. Use statistical software or a correlation table to find the P-value corresponding to r=0.987r = 0.987r=0.987 with the appropriate degrees of freedom.

STEP 7

Compare the P-value to the significance level α=0.05\alpha = 0.05α=0.05. If the P-value is less than α\alphaα, reject the null hypothesis.

STEP 8

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Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

1. We have data for pizza costs and subway fares for specific years.
2. We are testing for linear correlation between pizza costs and subway fares.
3. The significance level for hypothesis testing is $\alpha = 0.05$ .

Calculate the linear correlation coefficient $r$ . The given value is:
$r = 0.987$

Formulate the null and alternative hypotheses:
\begin{align} H_{0}: & \quad \rho = 0 \quad \text{(no linear correlation)} \\ H_{1}: & \quad \rho \neq 0 \quad \text{(linear correlation exists)} \end{align}

Determine the P-value for the calculated $r$ . Use statistical software or a correlation table to find the P-value corresponding to $r = 0.987$ with the appropriate degrees of freedom.

Compare the P-value to the significance level $\alpha = 0.05$ . If the P-value is less than $\alpha$ , reject the null hypothesis.