Question

(20.44) 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:

1.9	0.2	0.8	1.8	-0.2
2.2	-1.1	1.2	1.2	2.5

Take the data from these 10 carefully trained tasters as an SRS from a large population of all trained tasters.

Is there evidence at the 5% level that the cola lost sweetness? If the cola has not lost sweetness, the ratings after should be the same as before it was stored.

The test statisic is t =

Answer 1

From the given sample differences ,

The sample size , n=10

The sample mean is ,

The sample standard deviation is ,

Let , difference=before-after

The null and alternative hypothesis is ,

The test is right tailed test.

The test statistic is,

Now , df=degrees of freedom=n-1=10-1=9

The critical value is ,

; Form t-table

Decision : Here , the value of the test statistic lies in the rejection region.

Therefore , reject Ho.

Conclusion : There is sufficient evidence to conclude that the cola lost sweetness