- 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.

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
Pearson correlation of Max Daily Temperature (F) and Coffees = -0.741302
P-Value = <0.0001


3. Determine the p-value


4. Make a decision

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

5. State a "real world" conclusion.

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