please ve specific with the answer The owner of Briten\'s Egg Farm warts to estr

Question

please ve specific with the answer

The owner of Briten's Egg Farm warts to estrmate the mean number of eggs produced per chickan A ale ot 15 chickes shows thy produced an average of 24 eggu per month wth a standad deviaion of t What n the valu of the population mean? 0 24 a-2. What is the best estimoto of this au? stimate e. Fra99%centderoe iminal, what is the viku atf?(Round your answer lu 3 decimal places) Deveep te 99% tontdence rterval tor the populaton mean (Round your answer, Io 2 drental places.) d. -1.Would it be reasonable to concludo that e populat on mean s 22 egs e-2. What about 24 eg? O Yes

Explanation / Answer

Answer:

The owner of Britton’s Egg Farm wants to estimate the mean number of eggs produced per chicken. A sample of 15 chickens shows they produced an average of 24 eggs per month with a standard deviation of 6 eggs per month.

1. What is the value of the population mean?

The population mean would be the monthly mean number of eggs produced per chicken of all the chickens on the farm, but not just 20 of them. So the population mean is unknown.

2. What is the best estimate of the value?

The best estimate of the value of the population mean given only one sample’s average.

That is: 24 eggs per month.

3. For a 99 percent confidence interval, what is the value of t?

The degree of freedom is: 15-1 = 14 and the Confidence Interval is: 99%

Then the t – value is: 2.977

4. Develop the 99 percent confidence interval for the population mean.

The 99% confidence intervals for the population mean (E) is:

                E = 2.977[6/sqrt(15)]

                E = 2.977(1.5491)

                E = 4.6116

99% Confidence Interval: 24 – 4.6116 < u < 24 + 4.6116

Therefore, the lower confidence interval is: 19.3884; and

                the upper confidence interval is: 9.2232

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