# Small sample t-test for a population mean

Experience raising New Jersey Red chickens revealed the average weight of the chickens at age 5 months to be 4.35 lbs. The weights are normally distributed.

In an effort to increase their weight, a special additive was mixed with the chicken feed. The subsequent weights of a sample of five-month-old chickens were (in pounds): 4.41, 4.37, 4.33, 4.35, 4.30. Level of significance = 0.01.

1. Has the special additive increased the weight of the chickens?

2. State the hypothesis to be tested, the decision rule, the test statistic and the decision.

3. Estimate the p-value

4. In the context of your hypothesis, write out in words what making a type I error would mean.

Please provide detailed answers so that I can verify my answers and the calculations to my answers are proper/correct. Thank you.

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#### Solution Preview

I have attached a Word document with detailed calculations and explanations of all calculations for performing a small sample hypothesis test (t-test) regarding a population mean.

Experience raising New Jersey Red chickens revealed the average weight of the chickens at age 5 months to be 4.35 lbs. The weights are normally distributed.

In an effort to increase their weight, a special additive was mixed with the chicken feed. The subsequent weights of a sample of five-month-old chickens were (in pounds): 4.41, 4.37, 4.33, 4.35, 4.30. Level of significance = 0.01.

1. Has the special additive increased the weight of the chickens?

2. State the hypothesis to be tested, the decision rule, the test statistic and the decision.

3. Estimate the p-value

4. In the context of your hypothesis, write out in words what making a type I error would mean.

Please provide detailed answers so that I can verify my answers and the calculations to my answers are proper/correct. Thank you.

Solution

Detailed calculations are shown below. Verbal explanations are provided here.

1. Has the special additive ...

#### Solution Summary

This solution shows detailed hand calculations for performing a small sample hypothesis test (t-test) regarding a population mean.