Q. 71 - The Practice of Statistics for AP

Question

Sweetening colas Cola makers test new recipes for loss of sweetness during storage. Trained tasters rate the sweetness before and after storage. From experience, the population distribution of sweetness losses will be close to Normal. Here are the sweetness losses (sweetness before storage minus sweetness after storage) found by tasters from a random sample of $10$ batches of a new cola recipe:

$2.0 0.4 0.7 2.0 -0.4 2.2 -1.3 1.2 1.1 2.3$

Are these data good evidence that the cola lost sweetness? Carry out a test to help you answer this question.

Step-by-Step Solution

Answer

It appears that there is an average loss of sweetness for this cola.

Step 1: Given information

Here are the sweetness losses (sweetness before storage minus sweetness after storage) found by tasters from a random sample of $10$ batches of a new cola recipe:

$2.0 0.4 0.7 2.0 -0.4 2.2 -1.3 1.2 1.1 2.3$

Step 2: Explanation

State: $H_0 : \mu = 0 versus H_a : \mu < 0$, where $\mu$ is the actual mean amount of sweetness loss.

Plan: One-sample t test for $\mu$. 

Random: The sample was randomly selected. 

Normal: Previous experience tells us that sweetness losses will be close to Normal. Independent: There are at least $100$ batches of the new soda available. 

Do: $t = 2.70$, $P-value = 0.0122.$

Conclude: Since our P-value is less than $0.05$, we reject $H_0$.

It appears that there is an average loss of sweetness for this cola.