Exam 13: Inference Without Normality

Use the following information to answer the question. Math self-efficacy can be defined as one's belief in his or her own ability to perform mathematical tasks. A college math professor wishes to find out if her male students' math self-efficacy matches reality. To do this she gives a math quiz to the male students then asks them to rate their level of confidence in how well they did on the quiz. She plans to test whether those who had little confidence that they did well on the quiz actually performed worse than those who had a high level of confidence that they did well on the quiz. Shown below is the approximate sampling distribution of the difference in mean quiz scores. The table below shows the summary statistics for the two groups. Assume that all conditions for a randomization test have been satisfied. Group Mean Median Standard Deviation IQR High Conf. 105 82.5 84.0 7.1 12.5 Low Conf. 201 72.1 69.9 6.2 10.4 Test Stat: Mean High Conf. - Mean Low Conf. Number of simulations: 350 -Explain how you would use the histogram to get an approximate p-value and state your p-value estimation.

Which of the following statements is not true about the sign test?

Use the following information to answer the question. Math self-efficacy can be defined as one's belief in his or her own ability to perform mathematical tasks. A college math professor wishes to find out if her students' math self-efficacy matches reality. To do this she gives a math quiz then asks her students to rate their level of confidence in how well they did on the quiz. She plans to test whether those who had little confidence that they did well on the quiz actually performed worse than those who had a high level of confidence that they did well on the quiz. Shown below is the approximate sampling distribution of the difference in mean quiz scores. The table below shows the summary statistics for the two groups. Assume that all conditions for a randomization test have been satisfied. Group Mean Median Standard Deviation IQR High Conf. 106 78.6 77.5 5.5 9.5 Low Conf. 211 73.2 72.5 4.2 8.3 Test Stat: Mean High Conf. - Mean Low Conf. Number of simulations: 350 -Use the histogram to roughly estimate the p-value. Choose the answer that most closely approximates the p-value. (Approximations have been made to the nearest hundredth.)

A used car lot owner wanted to estimate the amount spent by customers during the summer months. She took a random sample of customers and recorded the amount they spent. A histogram Showed the data was right-skewed so she took the log of each value and verified that the Distribution of these values was more Normally distributed. What test/method should she use to Estimate the mean amount spent during the summer months?

Use the following information to answer the question. Math self-efficacy can be defined as one's belief in his or her own ability to perform mathematical tasks. A college math professor wishes to find out if her students' math self-efficacy matches reality. To do this she gives a math quiz then asks her students to rate their level of confidence in how well they did on the quiz. She plans to test whether those who had little confidence that they did well on the quiz actually performed worse than those who had a high level of confidence that they did well on the quiz. Shown below is the approximate sampling distribution of the difference in mean quiz scores. The table below shows the summary statistics for the two groups. Assume that all conditions for a randomization test have been satisfied. Group Mean Median Standard Deviation IQR High Conf. 106 78.6 77.5 5.5 9.5 Low Conf. 211 73.2 72.5 4.2 8.3 Test Stat: Mean High Conf. - Mean Low Conf. Number of simulations: 350 -Carry out the randomization test. What is the professor's conclusion? Are differences in mean quiz scores due to chance?

Suppose you are asked to analyze sample data but you do not know the distribution of the population it came from. Explain how a QQ plot can be used to give you information about the population from which the samples was drawn.

Which of the following statements is not true about the sign test?

State the null and alternative hypothesis to test the claim that dogs can affect anxiety levels.

Use the histogram to roughly estimate the p-value. Choose the answer that most closely approximates the p-value. (Approximations have been made to the nearest hundredth.)

Use the following information to answer the question. Suppose the Nielson Organization conducted a survey to find out how many minutes of reality-type television programming people watched in one week. Assume that all conditions for the Mann-Whitney test have been met. Use the following test output to answer the question. Hypothesis test results: $\mathrm{ml}=$ median for women $\mathrm{m} 2=$ median for men Parameter: m1-m2 Difference 1 2 Diff.Est Test Stat P-value Method 1-2 10 10 50 38.2 0.022 Norm. Approx. -Choose the correct null and alternative hypothesis to test the claim that men and women watch different amounts of reality-type programming.

Describe some conditions that might indicate that sign test should be used for inference.

Suppose data was collected from ten women and twelve men about the length in minutes of their commute to work. The histogram for men was roughly normal, but the histogram for women was strongly skewed to the right. Explain why the t-test is not appropriate to test whether men and women have different commute times.

Choose the statement that is not true about the Mann-Whitney Test.

Use the following information to answer the question. Can dogs lower anxiety in math class? Fifty subjects who reported anxiety about attending math class were measured for stress at the beginning of a math class then spent 15 minutes interacting with a dog followed by a forty-five minute math lecture. Each subject was then measured for stress at the end of the lecture. The hypothesis test results for the sign test are summarized below. Assume that all conditions for testing have been met: Hypothesis test results: Parameter: Median of variable : median =0 : median 0 Variable for tests Sample Median Below Equal Above P-value Difference 50 46 1 18 4 28 0.1839 -Explain how the binomial model is used to calculate the p-value.

Use the following information to answer the question. Can stretching help you stay alert in class? Thirty-six subjects were measured for alertness at the beginning of class; the subjects then participated in some light arm and neck stretches followed by a forty-five minute lecture. Each subject was then measured for alertness at the end of the lecture. The hypothesis test results for the sign test are summarized below. Assume that all conditions for testing have been met: Hypothesis test results: Parameter: Median of variable : median =0 : median 0 Variable for tests Sample Median Below Equal Above P-value Difference 36 32 1 12 4 20 0.2153 -Choose the correct null and alternative hypothesis.

List three of the five conditions, pertaining to the sample, which must be met in order to use the Mann-Whitney test.

A new fiber bar is advertised to curb hunger for three hours. A sample of thirty-six hungry subjects were asked to record their level of hunger before eating the fiber bar and again three hours after Eating the fiber bar. Which test should be used to test the hypothesis there is no difference in the Level of hunger three hours after eating the fiber bar (i.e. the fiber bar curbed hunger for three Hours)?

Use the following information to answer the question. Can stretching help you stay alert in class? Thirty-six subjects were measured for alertness at the beginning of class; the subjects then participated in some light arm and neck stretches followed by a forty-five minute lecture. Each subject was then measured for alertness at the end of the lecture. The hypothesis test results for the sign test are summarized below. Assume that all conditions for testing have been met: Hypothesis test results: Parameter: Median of variable : median =0 : median 0 Variable for tests Sample Median Below Equal Above P-value Difference 36 32 1 12 4 20 0.2153 -Using a significance level of 5%, state the correct decision regarding the null hypothesis and the concluding statement.

Which of the following QQ plots most closely depicts data from a skewed population?

Which of the following statements could be a reason to justify the use of the sign test?