Answer to Question #241098 in Statistics and Probability for darv

Question

A company which sells biscuits claims “Contents 880 grams” on the package. A sample of 28 packages yields an average of 800 grams. From past experience, the population standard deviation has been 50 grams. Using a .05 significance level, what conclusions would be drawn concerning the standard which the company is trying to achieve?

Answer 1

Null hypothesis: $u=880$

Alternative hypothesis: $u\not =880$

Since the sample size is small(<30), it is appropriate to use t-statistics

Also, the alternative hypothesis is $u\not =800$, so two-sided test is required

Test statistic: $T(27)={\frac {(800-880)*\sqrt{28}} {50}}=-8.46$

Critical value can be found in tables for t-statistic, it is equal to -2,052

Since value of test statistic is (<0) and smaller than critical value, it means that null hypothesis should be rejected.

There is a significant evidence that company claim is not true, the real mean weight is smaller than company claims.