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# Testing hypotheses based on a given data set

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1.
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):
4.41 4.37 4.33 4.35 4.30 4.39 4.36 4.38 4.40 4.39
At the .01 level, has the special additive increased the mean weight of the chickens?
Estimate the p-value.

2.
A recent article in theWall Street Journal reported that the prime rate for large banks now exceeds
9 percent. A sample of eight small banks in the Midwest revealed the following prime rates (in
percent):
10.1 9.3 9.2 10.2 9.3 9.6 9.4 8.8
At the .01 significance level, can we conclude that the prime rate for small banks also
exceeds 9 percent? Estimate the p-value.

##### Solution Summary

The solution contains detailed explanation of testing hypotheses using the five-step procedures.

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###### Education
• BSc , Wuhan Univ. China
• MA, Shandong Univ.
###### Recent Feedback
• "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
• "excellent work"
• "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
• "Thank you"
• "Thank you very much for your valuable time and assistance!"

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