A new-age, urban farmer has been experimenting with a new diet for her chickens. Data below describethe weight in kg from a sample of chickens from the current flock.1.6.57, 6.67, 6.98. 6.17, 6.17, 6.93. 6.73. 6.87, 6.76. 6.06, 6.16a. Do these data appear to be consistent with a normal distribution?b. Assuming a 0.05, is there sufficient evidence to reject the null hypothesis that H 6.50 kg?c. What is the P-value for this test?d. In the previous test, what sample size would be required to detect a true mean 6.25 kg withprobability 95%?For the test conducted in part a, what would be the type ll error probability if the true mean-6.95 kg?e.

Question
Asked Mar 9, 2019

Please answer d and e.

A new-age, urban farmer has been experimenting with a new diet for her chickens. Data below describe
the weight in kg from a sample of chickens from the current flock.
1.
6.57, 6.67, 6.98. 6.17, 6.17, 6.93. 6.73. 6.87, 6.76. 6.06, 6.16
a. Do these data appear to be consistent with a normal distribution?
b. Assuming a 0.05, is there sufficient evidence to reject the null hypothesis that H 6.50 kg?
c. What is the P-value for this test?
d. In the previous test, what sample size would be required to detect a true mean 6.25 kg with
probability 95%?
For the test conducted in part a, what would be the type ll error probability if the true mean-
6.95 kg?
e.
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A new-age, urban farmer has been experimenting with a new diet for her chickens. Data below describe the weight in kg from a sample of chickens from the current flock. 1. 6.57, 6.67, 6.98. 6.17, 6.17, 6.93. 6.73. 6.87, 6.76. 6.06, 6.16 a. Do these data appear to be consistent with a normal distribution? b. Assuming a 0.05, is there sufficient evidence to reject the null hypothesis that H 6.50 kg? c. What is the P-value for this test? d. In the previous test, what sample size would be required to detect a true mean 6.25 kg with probability 95%? For the test conducted in part a, what would be the type ll error probability if the true mean- 6.95 kg? e.

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Expert Answer

Step 1

The formula for confidence interval for t distribution is shown below

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Step 2

Here for the given sample, sample mean is 6.55, sample standard deviation is 0.347 and let the sample size be n. The critical t score for 95% confidence interval is 2.228 as shown below.

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Step 3

Now to detect a true mean 6.25 with 95% confidence interval the confidence interval should have the true mean value with in its boundaires. from the confidence interval formula we can say if the sample size increases the margin of error decrease, so as the deviation from sample mean in confidence interval. So this is possible if the lower boundary of the confidence interval is equa...

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