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1n hypothesis test. What formula do I use? How do I know what formula to use?

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Boys mean weight of 85lb. Complaint is made that in a children's home the boys are underfed. As one bit of evidence, all 25 boys of the given age are weighted and found to have a mean weight of 80.94. conclusion regarding complaint? SD=11.6, a = 0.05

Mar 26th, 2015

You are given sample mean and sample standard deviation and sample size is small.

You have to test the hypothesis regarding the mean

You must use t test.

degrees of freedom =25-1 =24

H0: mu =85

Ha: mu ≠ 85

Mu =85

Xbar =80.94

s= 11.6

n =25

t = (xbar-mu)/(s/√n)

t= (80.94-85)*5/11.6 = -4.06*5/11.6 = -20.3/11.6= -7/4 =-1.75

t value ( 2 tailed) = 2.064

Since |t | =1.75 < 2.064, we do not reject the null hypothesis

If you use one sided alternative

Ha: mu <  85

Then t value (1 tailed) = 1.711

Since - 1.75 < -1.71 

we will reject the null hypothesis in favor of the alternative hypothsis

Since there is a mention of "underfed" 

it is better to go for one sided alternative.

So we conclude that the complaint is justified. 

Mar 26th, 2015

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