12.2.1.3 - Example: Temperature & Coffee Sales

12.2.1.3 - Example: Temperature & Coffee Sales

Data concerning sales at student-run cafe were retrieved from cafedata.xls more information about this data set available at cafedata.txt. Let's determine if there is a statistically significant relationship between the maximum daily temperature and coffee sales.

CAFEDATA.XLS CAFEDATA.TXT

For this example, you can use the following Minitab file: cafedata.mpx

1. Check assumptions and write hypotheses

Maximum daily temperature and coffee sales are both quantitative variables. From the scatterplot below we can see that the relationship is linear.

Scatterplot of Coffees vs Max Daily Temperature (F)

\(H_0: \rho = 0\) 
\(H_a: \rho \neq 0\)

2. Calculate the test statistic

From Minitab:

Pairwise Pearson Correlations

Sample 1

Sample 2

N

Correlation

95% CI for \(\rho\)

P-Value

Max Daily Temperature (F)

Coffees

47

-0.741

(-0.848, -0.577)

0.000

\(r=-0.741\)

3. Determine the p-value

\(p=.000\)

4. Make a decision

\(p \leq \alpha\) therefore we reject the null hypothesis.

5. State a "real world" conclusion.

There is convincing evidence of a relationship between the maximum daily temperature and coffee sales in the population.

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