An experiment was conducted to determine whether there was a difference in the a

Question

An experiment was conducted to determine whether there was a difference in the average weights of the combs of roosters fed two different vitamin-supplement diets. Twenty-eight healthy roosters were randomly divided into two groups, with one group receiving diet I and the other receiving diet II. After the study period, the comb weight (in milligrams) was recorded for each rooster. The output is given here: Answer the following questions based on the output above: a. State the null and alternative hypotheses for this problem. b. What is the test statistic? P-value? c. State your conclusion in terms of the problem using a significance of 0.01. d. Based on the output, what is a 99% confidence interval for the difference in comb weights between the two groups?

Explanation / Answer

a) Let mu(diet1) represent the mean of diet1 roosters and mu(diet2) represent the diet2 mean

Null hypothesis H0: mu1 = mu2

There is no difference in the weights of roosters for 2 diets

Alternate hypothesis, H1: mu1 != mu2.

There is difference in the weights of roosters for 2 diets

b) test statistic = 4.069

p-value = t(4.069,26) = 0.00039 (given as 0.000 in the table under sig 2 tailed header)

c) alpha = 0.01

since p-value < 0.01, we can reject null hypothesis and state that there IS significant difference between the roosters of diet1 and diet 2

d) 99% confidence interval for (mu1-mu2)

99% upper confidence level value = 54.9371

99% lower confidence level value = 10.3485

which means we are 99% confident that the difference between the weight of rooster via 2 diets lies between 10.35 and 54.94

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