Question

In: Statistics and Probability

1 . The Food and Drug Administration has decided if a particular food product has 8...

1 . The Food and Drug Administration has decided if a particular food product has 8 grams or more of impurities it should be banned. A random sample of 36 cans of Tomato soup produced by Classic Food, Inc. showed 7.4 grams of impurities with a standard deviation of 3 grams. Test the hypothesis at the 1% level of significance. Please show the process of getting the answer

2. A production process is designed to fill cans with exactly 32 ounces of chicken noodle soup. A random sample of 49 cans was selected and inspected. The average weight of the cans in the sample is 31.9 ounces with a standard deviation of 0.5. Test the hypothesis at a 2% level of significance.  Please show the process of getting the answer

Solutions

Expert Solution

1 ) Given : Sample size=n=36

Sample mean=7.4

Sample standard deviation=s=3

Significance level=0.01

Population mean=8

Hypothesis:    VS

The test statistic under Ho is ,

Critical value : Since , the test is left tailed test

Decision : Here ,

Therefore , fail to reject Ho at 1% level of significance

Conclusion : Hence , there is sufficient evidence to conclude that the food and drug administration has decided the production should be banned.

2 ) Given : Sample size=n=49

Sample mean=31.9

Sample standard deviation=s=0.5

Significance level=0.02

Population mean=32

Hypothesis:    VS

The test statistic under Ho is ,

Critical value :

Decision : Here ,

Therefore , fail to reject Ho at 2% level of significance

Conclusion : Hence , there is sufficient evidence to conclude that the production process is designed to fill cans with exactly 32 ounces of chicken noodle soup

orchestra answered 2 years ago
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