Exam 8: Paired Data: One Quantitative Variable

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. -Which scenario in the Theory-Based Inference applet would you use for these data?

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. -Do you have evidence that the people in the appropriate group identified in question 28 are not accurate in their self-perception of attractiveness?

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. Which best describes this study design?

A Pew Research Center poll randomly selected and surveyed 2,002 US adults in the 25-32 age group and asked about their annual income. They found strong evidence that the unemployment rate for people without a college degree was higher than the unemployment rate of those with a college degree. 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. -Which applet would you use to perform a hypothesis test for this scenario?

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. -Write the null and alternative hypotheses in proper notation.

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 p-value for these data is 0.0067. Would you consider the results of this study to be statistically significant at the 5% significance level? Select one.

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. -To what group can we apply the results of this study?

Researchers conducted a study in which they invited nutrition experts to an ice cream social. These experts were randomly given either a 17- or a 34-ounce bowl. They were then invited to serve themselves ice cream. The suspicion was that even nutrition experts would tend to take more ice cream when given a larger bowl. Which best describes this study design?

A 1997 study described in the European Journal of Clinical Nutrition compares the growth of a random sample of vegetarian and omnivorous children, ages 7 - 11, in Northwest England. One of the aspects on which the children were compared was their body mass index (BMI). Of the 50 vegetarian children in the study, the average BMI was 16.76 and the standard deviation was 1.91. Among the 30 omnivorous children in the study, the average BMI was 17.12 and the standard deviation was 2.23. 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. 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. -Use the Theory-Based Inference applet to calculate a 90% confidence interval for this study.

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. -Use the Theory-Based Inference applet to calculate a 99% confidence interval for this study.

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. Which best describes this study design?

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 p-value for these data is 0.0067. Select the most appropriate conclusion.

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. -A simulated null distribution from the Matched Pairs applet is shown below. What applet inputs should you choose to compute the p-value? Count the proportion of samples (choose one) A) Greater than B) Less than C) Beyond (fill in the blank) ___________ .

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. -The p-value for the simulation-based hypothesis test is less than 0.001. What is the appropriate conclusion?

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. -Use the Theory-Based Inference applet to calculate the p-value 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" to compare to the self-rating to determine whether or not college students are accurate in their self-perceptions. 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. -Write the null and alternative hypothesis using proper notation.

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. -Can we conclude that walking causes increased eNO levels in the group to which the conclusion applies?