Exam 8: Paired Data: One Quantitative Variable

Researchers are interested in investigating the effect of a drug that is to be used in the treatment of patients who have glaucoma (an eye disorder associated with high eye pressure). The goal of the drug is to reduce eye pressure. In a volunteer sample of 35 patients with glaucoma in both eyes, one eye of each patient was randomly assigned to this drug, and the other eye was given a placebo. After one week, the eye pressure was measured on each eye. The difference in eye pressure between the two eyes (drug - placebo) was measured for each patient. The sample mean difference in eye pressure was -1.21 mmHg (millimeters of mercury), and the sample standard deviation of the differences was 4.67 mmHg. -What are the null and alternative hypotheses for this scenario? Use drug - placebo for the direction of the difference.

Researchers are interested in investigating the effect of a drug that is to be used in the treatment of patients who have glaucoma (an eye disorder associated with high eye pressure). The goal of the drug is to reduce eye pressure. In a volunteer sample of 35 patients with glaucoma in both eyes, one eye of each patient was randomly assigned to this drug, and the other eye was given a placebo. After one week, the eye pressure was measured on each eye. The difference in eye pressure between the two eyes (drug - placebo) was measured for each patient. Which best describes this study design?

A past statistics project investigated how well college students perceive their own attractiveness. Twenty college students were recruited to participate in the study. As part of the study, each student rated their own attractiveness on a scale from 1 - 10. Each of the 20 participants also agreed to have their picture taken. All pictures were taken in similar lighting. In the second part of the study, a group of 79 college student volunteers (who were not part of the original group of 20) agreed to rate the attractiveness of each of the people in the pictures on a scale of 1 - 10. Researchers then averaged the attractiveness rating of the 79 "raters" (referred to as the societal rating) to compare to the self-rating to determine whether or not college students are accurate in their self-perceptions. Summary statistics are presented in the following table. -Using the null distribution in question 26, approximate the p-value for this test.

A past statistics project investigated how well college students perceive their own attractiveness. Twenty college students were recruited to participate in the study. As part of the study, each student rated their own attractiveness on a scale from 1 - 10. Each of the 20 participants also agreed to have their picture taken. All pictures were taken in similar lighting. In the second part of the study, a group of 79 college student volunteers (who were not part of the original group of 20) agreed to rate the attractiveness of each of the people in the pictures on a scale of 1 - 10. Researchers then averaged the attractiveness rating of the 79 "raters" (referred to as the societal rating) to compare to the self-rating to determine whether or not college students are accurate in their self-perceptions. The average difference in attractiveness ratings (self - societal) in the sample was 1.066 with a standard deviation of 1.507. A dotplot of these differences follows. -Would it be valid to use a theoretical approach to analyze these data?

Researchers are interested in investigating the effect of a drug that is to be used in the treatment of patients who have glaucoma (an eye disorder associated with high eye pressure). The goal of the drug is to reduce eye pressure. In a volunteer sample of 35 patients with glaucoma in both eyes, one eye of each patient was randomly assigned to this drug, and the other eye was given a placebo. After one week, the eye pressure was measured on each eye. The difference in eye pressure between the two eyes (drug - placebo) was measured for each patient. The sample mean difference in eye pressure was -1.21 mmHg (millimeters of mercury), and the sample standard deviation of the differences was 4.67 mmHg. -Using a significance level of 0.01, do we have significant evidence that the drug helps reduce eye pressure?

Patients with chronic obstruction pulmonary disease (COPD) volunteered to be tested for exhaled nitric oxide (eNO) while resting and after a 6 minute walk test. Each subject was measured under each condition, and the order of presentation (resting then walking or the other way around) was randomized. Researchers believe the eNO should be higher while walking than resting for COPD patients. The data are summarized in the table below. Assume each of the distributions of eNO - while walking, while resting, and the differences - is not heavily skewed. -Which of the following best describes the parameter of interest?

A past statistics project investigated how well college students perceive their own attractiveness. Twenty college students were recruited to participate in the study. As part of the study, each student rated their own attractiveness on a scale from 1 - 10. Each of the 20 participants also agreed to have their picture taken. All pictures were taken in similar lighting. In the second part of the study, a group of 79 college student volunteers (who were not part of the original group of 20) agreed to rate the attractiveness of each of the people in the pictures on a scale of 1 - 10. Researchers then averaged the attractiveness rating of the 79 "raters" (referred to as the societal rating) to compare to the self-rating to determine whether or not college students are accurate in their self-perceptions. The average difference in attractiveness ratings (self - societal) in the sample was 1.066 with a standard deviation of 1.507. A dotplot of these differences follows. -Based off of the standardized statistic in question 32, what is your conclusion?

Researchers randomly selected 36 children who had been identified as gifted from a large city. The IQ of each child and the IQ of the child's mother were measured. You will perform a statistical analysis to determine if IQs of gifted children tend to be higher than their mothers' IQ on average. The mean difference in IQ (child - mother) was 3.22 points, with a standard deviation of 7.41 points. A dotplot of these differences follows. -The standardized statistic for these data is 2.61. How would you use this value to find a theory-based p-value for the study?

Patients with chronic obstruction pulmonary disease (COPD) volunteered to be tested for exhaled nitric oxide (eNO) while resting and after a 6 minute walk test. Each subject was measured under each condition, and the order of presentation (resting then walking or the other way around) was randomized. Researchers believe the eNO should be higher while walking than resting for COPD patients. The data are summarized in the table below. Assume each of the distributions of eNO - while walking, while resting, and the differences - is not heavily skewed. -To what group does this conclusion apply?

The following summary statistics and two dotplots display data on 64 used textbooks. The price of each used textbook was recorded from the University of California, Los Angeles (UCLA) campus bookstore and from Amazon. -You would like to determine whether the prices of used textbooks purchased from the UCLA bookstore are, on average, higher than the prices of used textbooks purchased from Amazon. What would be the null and alternative hypotheses using appropriate notation?

A past statistics project investigated how well college students perceive their own attractiveness. Twenty college students were recruited to participate in the study. As part of the study, each student rated their own attractiveness on a scale from 1 - 10. Each of the 20 participants also agreed to have their picture taken. All pictures were taken in similar lighting. In the second part of the study, a group of 79 college student volunteers (who were not part of the original group of 20) agreed to rate the attractiveness of each of the people in the pictures on a scale of 1 - 10. Researchers then averaged the attractiveness rating of the 79 "raters" (referred to as the societal rating) to compare to the self-rating to determine whether or not college students are accurate in their self-perceptions. The average difference in attractiveness ratings (self - societal) in the sample was 1.066 with a standard deviation of 1.507. A dotplot of these differences follows. -Calculate the standard error of the sample mean difference in attractiveness ratings (self - societal).

A past statistics project investigated how well college students perceive their own attractiveness. Twenty college students were recruited to participate in the study. As part of the study, each student rated their own attractiveness on a scale from 1 - 10. Each of the 20 participants also agreed to have their picture taken. All pictures were taken in similar lighting. In the second part of the study, a group of 79 college student volunteers (who were not part of the original group of 20) agreed to rate the attractiveness of each of the people in the pictures on a scale of 1 - 10. Researchers then averaged the attractiveness rating of the 79 "raters" (referred to as the societal rating) to compare to the self-rating to determine whether or not college students are accurate in their self-perceptions. Summary statistics are presented in the following table. -Define the parameter of interest in the context of the problem.

The following summary statistics and two dotplots display data on 64 used textbooks. The price of each used textbook was recorded from the University of California, Los Angeles (UCLA) campus bookstore and from Amazon. -If you were to create a scatterplot of the 64 textbooks, where the textbook's price at the UCLA bookstore was plotted on the x-axis, and the textbook's price on Amazon was plotted on the y-axis, what would be the value of the correlation coefficient?

A random sample of medical records from 28 heart attack patients at a Boston hospital was used to better understand the relationship between cholesterol and heart failure. The cholesterol levels of heart attack patients were recorded at 2 days and at 14 days after the patient had a heart attack. Which best describes this study design?

Patients with chronic obstruction pulmonary disease (COPD) volunteered to be tested for exhaled nitric oxide (eNO) while resting and after a 6 minute walk test. Each subject was measured under each condition, and the order of presentation (resting then walking or the other way around) was randomized. Researchers believe the eNO should be higher while walking than resting for COPD patients. The data are summarized in the table below. Assume each of the distributions of eNO - while walking, while resting, and the differences - is not heavily skewed. -The p-value of the test is less than 0.0001. Write a conclusion in the context of the problem.

Researchers randomly selected 36 children who had been identified as gifted from a large city. The IQ of each child and the IQ of the child's mother were measured. You will perform a statistical analysis to determine if IQs of gifted children tend to be higher than their mothers' IQ on average. The mean difference in IQ (child - mother) was 3.22 points, with a standard deviation of 7.41 points. A dotplot of these differences follows. -Use the Theory-Based Inference applet to calculate a 95% confidence interval for this study.

A past statistics project investigated how well college students perceive their own attractiveness. Twenty college students were recruited to participate in the study. As part of the study, each student rated their own attractiveness on a scale from 1 - 10. Each of the 20 participants also agreed to have their picture taken. All pictures were taken in similar lighting. In the second part of the study, a group of 79 college student volunteers (who were not part of the original group of 20) agreed to rate the attractiveness of each of the people in the pictures on a scale of 1 - 10. Researchers then averaged the attractiveness rating of the 79 "raters" (referred to as the societal rating) to compare to the self-rating to determine whether or not college students are accurate in their self-perceptions. The average difference in attractiveness ratings (self - societal) in the sample was 1.066 with a standard deviation of 1.507. A dotplot of these differences follows. -Calculate the standardized statistic for these data.

Researchers randomly assigned patients with severe acne to one of two treatments: the standard topical antibiotic (our control) or a new antibiotic taken orally (the treatment). Six months later an evaluation of skin problems was made by a doctor who did not know which medication subjects had been given. Which best describes this study design?

The following summary statistics and two dotplots display data on 64 used textbooks. The price of each used textbook was recorded from the University of California, Los Angeles (UCLA) campus bookstore and from Amazon. -Which applet should you use to perform a simulation-based hypothesis test for these data?

Researchers randomly selected 36 children who had been identified as gifted from a large city. The IQ of each child and the IQ of the child's mother were measured. You will perform a statistical analysis to determine if IQs of gifted children tend to be higher than their mothers' IQ on average. The mean difference in IQ (child - mother) was 3.22 points, with a standard deviation of 7.41 points. A dotplot of these differences follows. -Which scenario in the Theory-Based Inference applet would you use for these data?