A herd of 1,500 cows was fed a special highprotein grain for a month. A random s

Question

A herd of 1,500 cows was fed a special highprotein grain for a month. A random sample of 29 were weighed and had gained an average of 6.7 pounds. If the standard deviation of weight gain for the entire herd is 7.1, test the hypothesis that the average weight gain per cow for the month was more than 5 pounds.

Note: the following process is how you should set up most hypothesis tests!

a)   Identify the type of test

b)   Identify if the problem deals with proportions or means

c)    Determine if the test is one-tailed or two-tailed (justify one-tailed tests briefly).

d)   State the null and alternative hypotheses

e)   Run the test, determine probability-scores, determine exact value or consult table

f)    State if you accept or reject the null hypothesis

g)    Answer the question!

Explanation / Answer

a. Here test we will use is t test as n=29<30

b. It is dealing with mean.

c. It's one tailed right tail

d. H0: mean=5 vs H1: mu>5

e. t =xbar-mu/(sd/sqrt(n))=6.7-5/(7.1/sqrt(29))=1.29

p value for this test score is 0.1

f. Now if p value <alpha we reject the null hypothesis but here as pvalue>alpha(0.05,0.01) we accept the null hypothesis.

g. Average weight gain per cow is 5 pounds

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