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# Review Questions: Answer the following questions in detail.1. Explain the notions of mathematical differences, managerially important differences, and statistical significance. Can results be statisti

Review Questions: Answer the following questions in detail.

1. Explain the notions of mathematical differences, managerially important differences, and statistical significance. Can results be statistically significant and yet lack managerial importance. Explain youranswer.2. Describe the steps in the procedure for testing hypotheses. Discuss the difference between a null hypothesis and an alternative hypothesis.3. What purpose does a scatter diagram serve?

4. The following ANOVA summary data are the result of a regression with sales per year (dependent variable)as a function of promotion expenditures per year (independent variable) for a toy company.F = MSA = 34,276MSE 4,721The degrees of freedom are 1 for the numerator and 19 for the denominator. Is the relationship statistically significant at " = .05? Comment on your answer.

5. The following three random samples are taken from three normal populations with respective means μ1μ1, μ2μ2, and μ3μ3, and the same variance σ2.σ2.

Sample 1Sample 2Sample 32302513725 13

- Find the combined sample size n.
- Find the combined sample mean x−−.x-.
- Find the sample mean for each of the three samples.
- Find the sample variance for each of the three samples.
- Find MST.MST.
- Find MSE.MSE.
- Find F=MST∕MSE.

Here are the formulas to help you solve:

The **combined sample size**:

n=n1+n2+ ⋅ ⋅ ⋅ +nKn=n1+n2+ · · · +nK

The **mean of the combined sample** of all n observations:

x−−=Σxn=n1x−−1+n2x−−2+ ⋅ ⋅ ⋅ +nKx−−Knx-=Σxn=n1x-1+n2x-2+ · · · +nKx-Kn

The **mean square for treatment**:

MST=n1(x−−1−x−−)2+n2(x−−2−x−−)2+ ⋅ ⋅ ⋅ +nK(x−−K−x−−)2K−1MST=n1(x-1−x-)2+n2(x-2−x-)2+ · · · +nK(x-K−x-)2K−1

The **mean square for error**:

MSE=(n1−1)s21+(n2−1)s22+ ⋅ ⋅ ⋅ +(nK−1)s2Kn−K

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