Exam 8: Paired Data: One Quantitative Variable

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. -Fill in the blanks with the appropriate inputs to the Theory-Based Inference applet for these data. n: ___(1)___ mean, X: ___(2)___ sample sd, s: ___(3)___

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. -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. -A simulated null distribution of sample statistics is shown below. Explain how you would use this distribution to calculate the p-value.

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. -What are the observational units?

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 the p-value 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. -Are theory-based methods valid for use on this data set? Assume that the distribution of differences in eye pressure is not strongly skewed.

Researchers randomly assigned participants who smoked but were hoping to quit using tobacco to one of two treatments: nicotine patch (our control) or a newly designed pill (the treatment). Six months later the participants reported whether they were able to quit smoking or not. 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. -What is the observed statistic we should use for our hypothesis test?