The owner of Britten’s Egg Farm wants to estimate the mean number of eggs produc

Question

The owner of Britten’s Egg Farm wants to estimate the mean number of eggs produced per chicken. A sample of 18 chickens shows they produced an average of 20 eggs per month with a standard deviation of 5 eggs per month. (Use t Distribution Table.) a-1. What is the value of the population mean? is it:   5, 20, It is unknown. a-2. What is the best estimate of this value?       c. For a 95% confidence interval, what is the value of t? (Round your answer to 3 decimal places.)      d. Develop the 95% confidence interval for the population mean. (Round your answers to 2 decimal places.)       e-1. Would it be reasonable to conclude that the population mean is 17 eggs? Yes No e-2. What about 18 eggs?

Explanation / Answer

Ans

(a) The population mean is not known. But the best estimate of the population is the sample mean, that is 20 eggs per month.

(b) Since the sample size is small (less than 30), we need to use the t- distribution. We make the assumption that the sample drawn is random and is the number of eggs is normally distributed.

(c) The degrees of freedom for the t- test is 18 - 1 = 17. The value of t for 95% confidence is ± 2.110.

(d) Standard error of the mean is SE = s/n = 2/18 = 0.4714

Width of the 95% confidence interval is W = t * SE = 2.110 * 0.4714 = 0.9946

The 95% confidence interval is [x-bar - W, x-bar + W] = [20 - 0.9946, 20 + 0.9946] = [19.0053, 20.9946]

(e) Since both 17 and 18 lie outside the confidence interval calculated above, it is not reasonable to conclude that the population mean is 17 eggs or 18 eggs.

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.