Hypothesis Testing and Variation in Data
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TRUE OR FALSE? (WITH JUSTIFICATION)
1. Supporting the null hypothesis would be possible only if we could prove it for 100% of all possible cases.
2. If the claim says that µ >200 and the sample mean is 215, we can say that the claim is true because it is obvious even without a formal test.
3. A Calculated Value of F = 3 are evidence that...
4. A value of r = -0.851 shows that there is very little relationship between the two variables being compared.
5. A value of r = 0.158 shows that there is very little relationship between the two variables being compared.
6. If a correlation coefficient of r = 0.642 was found between two variables in a sample of paired data that were measured in feet, the value of r would change if the data were converted to inches and r was computed again.
7. More variation should be expected between larger samples, which are apparent by the chi-square distribution.
8. A test of independence can be used to determine a cause-and-effect link between the variables being studied.
9. Using the F distribution for a one-way ANOVA, the degrees of freedom for the denominator will always exceed the degrees of freedom for the numerator.
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Solution Summary
This solution answers questions regarding hypothesis testing and assessing variance.
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1. Supporting the null hypothesis would be possible only if we could prove it for 100% of all possible cases.
F. Statistically, we choose a confidence level (95% or 99%) to test the null hypothesis. When the calculated (t or z) statistic is smaller than the critical value, we claim that the null hypothesis cannot be rejected at the confidence level. It is not necessary to choose 100%.
2. If the claim says that µ >200 and the sample mean is 215, we can say that the claim is true because it is obvious even without a formal test.
F. It is still necessary to run a formal test for the null hypothesis. Because we need to ...
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