1. When constructing a hypothesis test, a comparison of the critical values obta
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Question
1. When constructing a hypothesis test, a comparison of the critical values obtained from z & t distributions for the same level of significance we can say:
A. the z-critical value will always be smaller than the t-critical value, meaning the hypothesis test will require more evidence to reject the null hypothesis when the t-distribution is used
B. the z-critical value will always be larger than the t-critical value, meaning the hypothesis test will require more evidence to reject the null hypothesis when the z-distribution is used
C. we cannot compare the sizes of the critical values without knowing the degrees of freedom
D. the z-critical value will be the same size as the t-critical value
2. Which of the following is true about the critical value & test statistic?
A. if the critical value is in the rejection region of the graph, the null hypothesis must be rejected
B. the test statistic is calculated based on the observed sample data & is compared to the critical value to determine whether the sample provides sufficient evidence to reject the null hypothesis
C. a critical value is calculated based on the observed sample data & is compared to the test statistic to determine whether the sample provides sufficient evidence to reject the null hypothesis
D. none of the above
3. Which of the following is TRUE about the relationship between critical value, the test statistic, the level of significance of the hypothesis test, & the p-value (the observed level of significance)?
A. when conducting a hypothesis test, it is possible for the test statistic/critical value approach to result in a conclusion to reject the null hypothesis & for the p-value to still be larger than the level of significance of the test
B. since the level of significance of the test determines the size of the critical value & the test statistic is used to calculate the p-value, if the test statistic (in absolute value) is larger than the critical value, then the p-value will be larger than the level of significance specified
C. since the level of significance of the test determines the size of the critical value & the test statistic is used to calculate the p-value, if the test statistic falls in the rejection region, then the p-value will be smaller than the level of significance specified
D. none of the above
4. Which of the following is correct?
Statement I: when sampling from a population, if the population size is at least 30, it is possible the observed sample WILL NOT be normally distributed, but the sampling distribution for the sample mean WILL be normally distributed.
Statement II: The Central Limit Theorem guarantees that if the sample size is at least 30, then the values observed in the sample will be normally distributed.
A. Statement I only
B. Statement II only
C. Both Statements
D. Neither Statements
Explanation / Answer
1.
For t-critical value we need sample size so that we can find degree of freedom. With degree of freedom we cannot know t critical value and cannot compare it with z-crtical value. So option C is correct.
2.
B. the test statistic is calculated based on the observed sample data & is compared to the critical value to determine whether the sample provides sufficient evidence to reject the null hypothesis
3.
C. since the level of significance of the test determines the size of the critical value & the test statistic is used to calculate the p-value, if the test statistic falls in the rejection region, then the p-value will be smaller than the level of significance specified
4.
Option C is correct.
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