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# Sample Mean and Z-distribution

Experience raising New Jersey Red chickens revealed the mean weight of the chickens at five months is 4.35 pounds. The weights follow the normal distribution. In an effort to increase their weight, a special additive is added to the chicken feed. The subsequent weights of a sample of five-month-old chickens were (in pounds): (In all your following computations, use three decimal places.)

4.41 4.37 4.33 4.35 4.30 4.39 4.36 4.38 4.40 4.39

a. What is the sample mean of the weights of the chickens after being fed the new additive?

b. Would you use the Z-distribution or the Student-t distribution to develop a confidence interval for these data? Explain your choice.

c. Having made your selection of the appropriate probability distribution in part (b), what is the value of Z (or t) for a 95% confidence interval to test whether the additive has increased the weight of the chickens?

d. What is the 95% confidence interval for the population mean weight of the chickens after they were fed the new additive?

e. Based on your 95% confidence interval, discuss whether you can conclude that the mean weight of the chickens has statistically increased.

f. Does it make any difference to your conclusion in part (e) whether you used the normal distribution or the t-distribution? Explain.

g. Does it make any difference to your conclusion in part (e) whether you used a 90% confidence interval instead of a 95% confidence interval? Explain

#### Solution Summary

The solution examines statistics for New Jersey Red Chickens.

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