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.

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.

$$H_0: \rho = 0$$
$$H_a: \rho \neq 0$$

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

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