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Categorizing Inference Questions

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Categorizing Inference Questions

Categorizing Inference Questions1. Infants who cry easily may be more easily stimulated than others. This may be a sign of higher IQ. Child development researchers explored the relationship between the crying of infants 4 to 10 days old and their later IQ test scores. A snap of a rubber band on the sole of the foot caused the infants to cry. The researchers recorded the crying and measured its intensity by the number of peaks in the most active 20 seconds. They later measured the childrens IQ at age 3 years. The table below contains data from a random sample of 38 infants. Do these data provide convincing evidence that there is a positive linear relationship between the cry counts and IQ in the population of infants?

The researchers recorded the crying intensity by the number of peaks in the most active 20 seconds. They later measured the childrens IQ at age 3 years. The table below contains data from a random sample of 38 infants. Do these data provide convincing evidence that there is a positive linear relationship between the cry counts and IQ in the population of infants?2. Trace metals found in wells affect the taste of drinking water, and high concentrations can pose a health risk. Researchers measured the concentration of zinc (in milligrams per liter) near the top and the bottom of 10 randomly selected wells in a large region. The data are provided in the table below. Construct and interpret a 95% confidence interval for the mean difference in the zinc concentrations from these two locations in the wells.

A) meansB) the mean difference in the zinc concentrations from these two locations in the wellsC) one sample of 10 wells - two measurements at each wellResearchers measured the concentration of zinc (in milligrams per liter) near the top and the bottom of 10 randomly selected wells in a large region. The data are provided in the table below. Construct and interpret a 95% confidence interval for the mean difference in the zinc concentrations from these two locations in the wells.3. Researchers designed a survey to compare the proportions of children who come to school without eating breakfast in two low-income elementary schools. An SRS of 80 students from School 1 found 19 had not eaten breakfast. At School 2, an SRS of 150 students included 26 who had not had breakfast. More than 1500 students attend each school. Do these data give convincing evidence of a difference in the population proportions?

A) proportionsB) the true difference in the population proportions of children who come to school without eating breakfast in two low income elementary schoolsC) two samplesResearchers designed a survey to compare the proportions of children who come to school without eating breakfast in two low-income elementary schools. An SRS of 80 students from School 1 found 19 had not eaten breakfast. At School 2, an SRS of 150 students included 26 who had not had breakfast. More than 1500 students attend each school. Do these data give convincing evidence of a difference in the population proportions?4. Bottles of a popular cola are supposed to contain 300 milliliters of cola. There is some variation from bottle to bottle because the filling machinery is not perfectly precise. From experience, the distribution of the contents of the bottles is approximately normal. An inspector measures the contents of six randomly selected bottles from a single days production. Do these data provide convincing evidence that the mean amount of cola in all the bottles filled that day differs from the target value of 300 ml?

A) meansB) the mean amount of cola in all the bottles filled that dayC) one sampleFrom experience, the distribution of the contents of the bottles is approximately normal. An inspector measures the contents of six randomly selected bottles from a single days production. Do these data provide convincing evidence that the mean amount of cola in all the bottles filled that day differs from the target value of 300 ml?5. Some doctors have begun to use medical magnets to treat patients with chronic pain. Scientists wondered whether this type of therapy really worked, so they designed an experiment to find out. Fifty patients with chronic pain were recruited for the study. A doctor identified a painful site on each patient and asked him or her to rate the pain on a scale from 0 to 10. Then, the doctor selected a sealed envelope containing a magnet from a box that contained both active and inactive magnets. The chosen magnet was applied to the site of the pain for 45 minutes. After treatment, each patient was again asked to rate the level of pain from 0 to 10. In all, 29 patients were given active magnets and 21 patients received inactive magnets. All but one of the patients rated their initial pain as 8, 9, or 10, so scientists decided to focus on the patients final pain ratings. Do these data show statistical evidence to suggest that the active magnets help reduce pain?In all, 29 patients were given active magnets and 21 patients received inactive magnets. All but one of the patients rated their initial pain as 8, 9, or 10, so scientists decided to focus on the patients final pain ratings. Do these data show statistical evidence to suggest that the active magnets help reduce pain?A) This question doesnt explicitly say whether its proportions or means, but there are no percentages, and we could find the mean pain rating, so it is means.B) The true reduction(difference) in mean pain rating for patients using magnets as opposed to a placeboC) Two samples even though there were 50 patients originally, they get split into two separate treatments. Since whether they get the magnet or not is random, we can say the two samples are independentIn all, 29 patients were given active magnets and 21 patients received inactive magnets. All but one of the patients rated their initial pain as 8, 9, or 10, so scientists decided to focus on the patients final pain ratings. Do these data show statistical evidence to suggest that the active magnets help reduce pain?7. A local high school makes a change that should improve student satisfaction with the parking situation. Before the change, 37% of the schools students approved of the parking that was provided. After the change, the principal surveys an SRS of 200 of the over 2500 students at the school. In all, 83 students say that they approve of the new parking arrangement. Is this evidence that the change was effective?A) Proportions you have a % and fraction 83/200B) The true difference in proportion of students satisfied with the parking situation before and after the change.C) Two samples of studentsBefore the change, 37% of the schools students approved of the parking that was provided. After the change, the principal surveys an SRS of 200 of the over 2500 students at the school. In all, 83 students say that they approve of the new parking arrangement. Is this evidence that the change was effective?10. Breast-feeding mothers secrete calcium into their milk. Some of the calcium may come from their bones, so mothers may lose bone mineral. Researchers compared a random sample of 47 breast-feeding women with a random sample of 32 women of similar age who were neither pregnant nor lactating. They measured the percent change in the bone mineral content of the womens spines over three months. Comparative data is given below. Is the mean change in bone mineral content significantly lower for the mothers who are breast-feeding?A) meansB) the true difference in the mean change of bone mineral content between breast feeding women and those not breastfeedingResearchers compared a random sample of 47 breast-feeding women with a random sample of 32 women of similar age who were neither pregnant nor lactating. They measured the percent change in the bone mineral content of the womens spines over three months. Comparative data is given below. Is the mean change in bone mineral content significantly lower for the mothers who are breast-feeding?One researcher took the oral temperature reading for each of 130 randomly chosen, healthy 18- to 40-year olds. The mean temperature was 98.25oF, with a standard deviation of 0.73oF. Do these data provide convincing evidence that normal body temperature is not 98.6oF?E) Assumptions unknown, use tRandom sample of healthy 18- to 40-year-olds givenSince the sample size is greater than 30, we can use a normal approximationPopulation of 18- to 40-year-olds > 130012. A study followed a random sample of 8474 people with normal blood pressure for about four years. All the individuals were free of heart disease at the beginning of the study. Each person took a test which measures how prone a person is to sudden anger. Researchers also recorded whether each individual developed coronary heart disease. Do the data provide convincing evidence of an association between anger level and heart disease in the population of interest?A) categorical dataB) whether there is an association between anger level and heart disease in the population of adultsC) one sample two variables A study followed a random sample of 8474 people with normal blood pressure for about four years. All the individuals were free of heart disease at the beginning of the study. Each person took a test which measures how prone a person is to sudden anger. Researchers also recorded whether each individual developed coronary heart disease. Do the data provide convincing evidence of an association between anger level and heart disease in the population of interest?A drug manufacturer claims that less than 10% of patients who take its new drug for treating Alzheimers disease will experience nausea. To test this claim, researchers conduct an experiment. They give the new drug to a random sample of 300 out of 5000 Alzheimers patients whose families have given informed consent for the patients to participate in the study. In all, 25 of the subjects experience nausea.E) AssumptionsRandom sample of 300 Alzheimers patients - givenn1p1 = 25 n1(1-p1) - 275 Since both of these values are >10 we can use a normal approximationPopulation of Alzheimers patients > 300015. Market researchers suspect that background music may affect the mood and buying behavior of customers. One study in a supermarket compared three randomly assigned treatments: no music, French accordion music, and Italian string music. Under each condition, the researchers recorded the numbers of bottles of French, Italian, and other wine purchased. Are the distributions of wine purchases under the three music treatments similar or different?A) categorical dataB) if the population of customers has the same buying habits with different music treatmentsC) 3 samples (treatment groups)One study in a supermarket compared three randomly assigned treatments: no music, French accordion music, and Italian string music. Under each condition, the researchers recorded the numbers of bottles of French, Italian, and other wine purchased. Are the distributions of wine purchases under the three music treatments similar or different?16. A surprising number of young adults (ages 19 to 25) still live in their parents homes. The National Institutes of Health planned to estimate the difference in proportions of women and men in this age group who live at home. The random sample included 2253 men and 2629 women in this age group. The survey found that 986 of the men and 923 of the women lived with their parents.

A) proportionsB) the true difference in proportions of men and women ages 19 25 who still live with their parentsC) two samples men and women

The National Institutes of Health planned to estimate the difference in proportions of women and men in this age group who live at home. The random sample included 2253 men and 2629 women in this age group. The survey found that 986 of the men and 923 of the women lived with their parents.17. The Wade Tract Preserve in Georgia is an old-growth forest of long-leaf pines that has survived in a relatively undisturbed state for hundreds of years. One question of interest to foresters who study the area is How do the sizes of long-leaf pine trees in the northern and southern halves of the forest compare? To find out, researchers took random samples of 30 trees from each half of the forest and measured the trees diameter in centimeters. What is the difference in mean diameters of long-leaf pines in the northern and southern halves?A) mean its not proportions, and we can find the mean diameterB) the true difference of the mean diameters of trees in the northern and southern halves of the Wade Tract PreserveTo find out, researchers took random samples of 30 trees from each half of the forest and measured the trees diameter in centimeters. What is the difference in mean diameters of long-leaf pines in the northern and southern halves?18. Environmentalists, government officials, and vehicle manufacturers are all interested in studying the auto exhaust emissions produced by motor vehicles. The major pollutants in auto exhaust from gasoline engines are hydrocarbons, carbon monoxide, and nitrogen oxides (NOX). Researchers collected data on the NOX levels (in grams per mile) for a random sample of 40 light-duty engines of the same type. The mean NOX reading was 1.2675 and the standard deviation was 0.3332.A) meansB) The true mean NOX level of the population of light-duty enginesC) one sampleResearchers collected data on the NOX levels (in grams per mile) for a random sample of 40 light-duty engines of the same type. The mean NOX reading was 1.2675 and the standard deviation was 0.3332.19. Do experienced computer game players earn higher scores when they play with someone present to cheer them on or when they play alone? Fifty teenagers who are experienced at playing a particular computer game have volunteered for a study. We randomly assign 25 of them to play the game alone and the other 25 to play the game with a supporter present. Each players score is recorded.A) means (mean score)B) the true difference in the mean scores of players with and without a supporter presentC) two samples (or randomly assigned groups)

Fifty teenagers who are experienced at playing a particular computer game have volunteered for a study. We randomly assign 25 of them to play the game alone and the other 25 to play the game with a supporter present. Each players score is recorded.20. As part of the Pew Internet and American Life Project, researchers conducted two surveys in late 2009. The first survey asked a random sample of 800 U.S. teens about their use of social media and the Internet. A second survey posed the same questions to a random sample of 2253 U.S. adults. In these two studies, 73% of teens and 47% of adults said that they use social-networking sites. Construct and interpret a 95% confidence interval for the difference in the proportion of all US teens and adults who use social-networking sites.A) proportionsB) the true difference in the proportion of US teens and adults who use social-networking sitesThe first survey asked a random sample of 800 U.S. teens about their use of social media and the Internet. A second survey posed the same questions to a random sample of 2253 U.S. adults. In these two studies, 73% of teens and 47% of adults said that they use social-networking sites. Construct and interpret a 95% confidence interval for the difference in the proportion of all US teens and adults who use social-networking sites.