True of false. On the line provided identify if the statement is true or false.

Question

True of false. On the line provided identify if the statement is true or false.

1. If the null hypothesis if rejected, then the alternative hypothesis is supported.

2. The population mean is equal to the mean of the sampling distribution.

3. Both the t and F tests require the assumption that the population sampled is normal.

4. As the number of degrees of freedom increaes, the chi-square distribution approaches an F distribution.

5. If the null hypothesis (two tailed test) is tested at 1%, then the critical values includes the middle 99% of the values.

6. An increase in the sample size will increase the standard error.

7. Alpha is the probability of a Type I Error.

8. If alpha is chosen to be 5%, and the p-value for a hypothesis test is 0.047, then the null hypothesis should be rejected.

9. In a goodness of fit hypothesis test, a large chi-square value will cause the null hypothesis test not to be rejected.

10. In a chi-square test of independence, a rejection of the null hypothesis means that there is not a relationship betweeen the two categorical variables.

Explanation / Answer

1. If the null hypothesis if rejected, then the alternative hypothesis is supported. [TRUE]

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2. The population mean is equal to the mean of the sampling distribution. [TRUE, by central limit theorem]

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3. Both the t and F tests require the assumption that the population sampled is normal. [FALSE.]

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4. As the number of degrees of freedom increaes, the chi-square distribution approaches an F distribution.

[FALSE. It is the other way around, the F distribution approaches a chi-square distribution]

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5. If the null hypothesis (two tailed test) is tested at 1%, then the critical values includes the middle 99% of the values.

[FALSE. It includes the outer 1% of the values.]

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