QAS FINAL STUDY GUIDE

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Statistics

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Apr 3, 2024

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Which of the following questions can be used to draw conclusions from a test of significance? A) If p is less than the significance level alpha, then reject the null hypothesis. B) If p is greater than the significance level alpha, then reject the null hypothesis. C) If the P-value is less than the significance level alpha, then reject the null hypothesis. D) If the P-value is greater than the significance level alpha, then reject the null hypothesis. The p-value represents the probability of observing the data or more extreme results if the null hypothesis is true. If the p-value is less than the chosen significance level (often denoted as alpha), it suggests that the observed data is unlikely to have occurred under the assumption that the null hypothesis is true. Therefore, in such cases, the null hypothesis is rejected in favor of the alternative hypothesis. *********************** In a test of hypothesis, a small P-value provides evidence: A small p-value indicates that the observed data is unlikely to have occurred if the null hypothesis were true. Therefore, it suggests that there is strong evidence against the null hypothesis, leading to its rejection in favor of the alternative hypothesis. This supports the conclusion that there is a statistically significant difference or effect present in the data. a. against the null hypothesis in favor of the alternative hypothesis. A small p-value indicates that the observed data is unlikely to have occurred if the null hypothesis were true. Therefore, it provides evidence against the null hypothesis, supporting the conclusion in favor of the alternative hypothesis. The four steps in a hypothesis test are typically: 1. State the Hypotheses : This step involves clearly stating the null hypothesis (H0) and the alternative hypothesis (Ha or H1). The null hypothesis typically represents the status quo or no effect, while the alternative hypothesis represents what the researcher is trying to find evidence for. 2. Formulate a Test Statistic and Sampling Distribution : In this step, you identify an appropriate test statistic based on the type of data and hypothesis being tested. You also determine the sampling distribution under the assumption that the null hypothesis is true. 3. Determine the Decision Rule and Compute the Test Statistic : This step involves determining the criteria for rejecting the null hypothesis, typically based on a significance level (alpha) and the distribution of the test statistic. You then compute the test statistic using the observed data.

4. Make a Decision and Interpret Results : Finally, you compare the test statistic to the critical value(s) or use the p-value to make a decision about whether to reject or fail to reject the null hypothesis. You interpret the results of the test in the context of the research question and draw conclusions based on the evidence from the hypothesis test. So, the correct steps are:  State  Identify (Formulate a Test Statistic and Sampling Distribution)  Determine (Determine the Decision Rule and Compute the Test Statistic)  Verify (Make a Decision and Interpret Results) *********************** Which of the following is known for the P-value, if a hypothesis test is significant at level = 0.05? Group of answer choices P-value 0.05 P-value > 0.05 P-value 0.01 P-value > 0.01 If a hypothesis test is significant at level α =0.05, it means that the p-value associated with the test is less than or equal to 0.05. Therefore, the correct choice is: P-value ≤ 0.05 *********************** A P-value is always computed assuming that: A) the alternative hypothesis is true. B) the alternative hypothesis may be true. C) the null hypothesis may be true. D) the null hypothesis is true. C) the null hypothesis may be true. The p-value is a measure of the strength of evidence against the null hypothesis. It represents the probability of observing the data or more extreme results if the null hypothesis were true. However, it does not assume that the null hypothesis is true; rather, it assesses the likelihood of the observed data under the assumption that the null hypothesis may be true. Therefore, the p-value is always computed assuming that the null hypothesis may be true. *********************** The p-value measures the strength of evidence: a) the interpretation depends on whether we reject the null hypothesis. b) against the alternative hypothesis.

c) sometimes against the null hypothesis and sometimes against the alternative hypothesis. d) against the null hypothesis The p-value measures the strength of evidence against the null hypothesis. However, whether the evidence is considered in favor of or against the null hypothesis depends on the significance level (alpha) chosen for the hypothesis test. If the p-value is less than or equal to the significance level (alpha), it provides evidence against the null hypothesis, leading to its rejection in favor of the alternative hypothesis. Conversely, if the p-value is greater than the significance level, it does not provide sufficient evidence to reject the null hypothesis. So, the interpretation of the p-value depends on whether we reject the null hypothesis, making option (a) also partially correct. However, since the p- value can also provide evidence in favor of the null hypothesis, option (c) is the most comprehensive choice. In a test of statistical hypotheses, the p-value tells us: a) the largest level of significance at which the null hypothesis can be rejected. b) the smallest level of significance at which the null hypothesis can be rejected. c) if the alternative hypothesis is true. d) if the null hypothesis is true. d) if the null hypothesis is true. T he p-value tells us the probability of obtaining the observed data, or more extreme results, under the assumption that the null hypothesis is true. Therefore, it provides information about whether the null hypothesis is supported by the data or if there is evidence against it. If the p-value is very small, it suggests that the observed data is unlikely to have occurred if the null hypothesis were true, indicating evidence against the null hypothesis. Conversely, if the p-value is large, it suggests that the observed data is likely under the null hypothesis, providing weak evidence against it. Therefore, the p-value helps in assessing the validity of the null hypothesis. *********************** Which of the following is an acceptable statement of a null and alternative hypothesis for testing a hypothesis about a population mean? If all answers are correct, select the last option below. H0: µ = 10 vs Ha: µ > 10. H0: µ = 10 vs Ha: µ < 10. H0: µ = 10 vs Ha: µ ≠ 10. All of the answers are correct. Two students taking a multiple-choice exam with 20 questions and four choices for each question have the same incorrect answer on seven of eight incorrectly answered problems. The probability that student B guesses the same incorrect answer as student A on a particular question is 1/4. If the student is guessing, the guess for one problem is

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independent of the guess for the other problems. The probability of getting agreement on seven or more out of eight questions is:

QAS FINAL STUDY GUIDE

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