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# SSE's, SST's, F-ratio, ANOVA, and null hypothesis

Problem 1

An aircraft manufacturer is attempting to determine if the average leg length of the adult male has changed from 44". A sample of 81 men was selected randomly and the average length was found to be 45.5", with a standard deviation of 5.5". Test the null hypothesis that the average leg length of the adult male is 44", at & alpha = 0.05.

Problem 2

If Z = 1.96, standard deviation = 3, and B = 1, determine the correct sample size.

Problem 3

A marketing manager wants to determine if the advertising spending per month of his competitors is equal or not. Data over the last six months reveals the following figures (in thousands of dollars).

A B C
11 9 12
17 12 23
27 27 28
35 45 27
43 54 39
38 32 41

A.Calculate the SSE for these observations;
B.Compute the SST for these observations (answers below are rounded)
C.Calculate the F-ratio for the ANOVA based on these observations;
D.Find the F-value from the table in the back of the book to test the hypothesis that there is no difference in the average spending among these companies at alpha= 0.05

#### Solution Preview

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Solution

1.

An aircraft manufacturer is attempting to determine if the average leg length of the adult male has changed from 44". A sample of 81 men was selected randomly and the average length was found to be 45.5", with a standard deviation of 5.5". Test the null hypothesis that the average leg length of the adult male is 44", at &#61537; = 0.05.

n= 81

s=5.5"

Ho: Average length of adult male is 44"
H1: Average length of adult male is not 44"

It's a two tail test.

alpha = 0.05

Since population standard deviation is not given, we will use sample standard deviation as an estimate of population standard deviation.

Confidence interval will be

Standard error =

Let us standardize sample mean (observed Z)

Critical value of Z can be seen from the table at 0.05 level of significance. Z is -1.96 to 1.96. Our observed Z lies outside the critical range. We fail to accept null hypothesis at 5% significance level.

We can say statistics support that average ...

#### Solution Summary

There are three problems. Solution to first problem explains the steps in hypothesis testing for aircraft manufacture's claim that average leg lenght has changed.
For second problems, sample size is dertermined with the help of given tolerance limits.
For third problems, ANOVA analysis is carried out and specific questions asked related to this study are answered.

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