Question

C. Yields of ten randomly selected samples of bread from a factories were

23.9, 23.5, 20.6, 21.7, 23.4, 21.9, 21.0, 19.1, 22.5, and 24.8. Is there any reason to believe that the population mean yield of bread is significantly (? = 0.05)

different from 21.0.

Test Hypothesis:

Test statistics:

Critical value(s):

Conclusion:

Answer 1

Let denotes the population mean yield of bread.

To test against

Here

sample mean

sample standard deviation

and sample size

The test statistic can be written as

which under H₀ follows at distribution with n-1 df.

We reject H₀ at 0.05 level of significance if

Now,

The value of the test statistic =

and critical value =

Since , so we reject H₀ at 0.05 level of significance and we can conclude that population mean yield of bread is significantly different from 21.0.