20.44 Sweetening colas . Cola makers test new recipes for loss of sweetness duri
ID: 3153593 • Letter: 2
Question
20.44Sweetening colas. Cola makers test new recipes for loss of sweetness during storage. Trained tasters rate the sweetness before and after storage. Here are the sweetness losses (sweetness before storage minus sweetness after storage) found by 10 tasters for one new cola recipe:
2.0 0.4 0.7 2.0 –0.4 2.2 –1.3 1.2 1.1 2.3
Take the data from these 10 carefully trained tasters as an SRS from a large population of all trained tasters.
(a)Use these data to see if there is good evidence that the cola lost sweetness.
(b)It is not uncommon to see the t procedures used for data like these. However, you should regard the results as only rough approximations. Why?
Explanation / Answer
a)
Formulating the null and alternative hypotheses,
Ho: u <= 0
Ha: u > 0
As we can see, this is a right tailed test.
df = n - 1 = 9
Getting the test statistic, as
X = sample mean = 1.02
uo = hypothesized mean = 0
n = sample size = 10
s = standard deviation = 1.196104789
Thus, t = (X - uo) * sqrt(n) / s = 2.69668949
Also, the p value is
p = 0.012263156
As the P value is small (say, less than 0.05), we REJECT THE NULL HYPOTHESIS.
Hence, there is good evidence that the cola lost sweetness. [CONCLUSION]
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b)
It is because we assume here that the data came from an at least approximately normally distributed distribution. Since we usually don't prove the original distribution is approximately normal, then we only regard our results as rough approximations.
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