Statistics HW 1&2

Which of the following scatterplots exhibits a strong negative correlation?

(I only added this picture because the answer was obvious)

Given two correlation coefficients, -0.15 and 0.13, which one indicates a stronger relation between variables? A. -;0.15 is slightly stronger B. 0.13 is stronger C. 0.13 is slightly stronger D. -;0.15 is stronger

A. -;0.15 is slightly stronger

Which of the following statements about correlations is not true? A. A strong positive correlation implies that one of the variables very likely to have an effect on the other variable. B. The Pearson correlation coefficient is used to measure both the direction and the strength of linear relationships. C. In a negative correlation, as the value of the first variable increases, the value of the second variable decreases. D. In a positive correlation, as the value of the first variable increases the value of the second variable also increases.

A. A strong positive correlation implies that one of the variables very likely to have an effect on the other variable.

Type of frequency distribution: Suppose that you collected data on eye color for 87 people. How would you present these data values when creating a frequency distribution and why? A. Individual data values because there are not many possible values for eye color B. Individual data values because eye color is an ordinal variable C. Grouped data values because eye color is a nominal variable D. Grouped data values because there are too many data points for individual data

A. Individual data values because there are not many possible values for eye color

Statistics versus parameters: According to 2006 Canadian census data, the median family income in British Columbia was $62,346, lower than the national average of $63,866. Is the national average income a statistic or a parameter and why? A. Parameter; the census data includes all members of the population of interest, Canadians. B. Statistic; census data is drawn from a small number of individuals and then applied to a larger group. C. Statistic; the census data is being used as part of a comparison process. D. Parameter; mean values are always parameters.

A. Parameter; the census data includes all members of the population of interest, Canadians.

Statistics versus parameters: The National Survey of Student Engagement (NSSE) asked students at participating institutions how often they discussed ideas or readings with professors outside of class. Among the 19 national universities that made their data public, the mean percentage of U.S. students who responded "Very often" was 8%. Is the mean percentage a statistic or a parameter and why? A. Statistic; it is the mean percentage for the sample of schools that participated in the NSSE, not all schools in the United States. B. Parameter; the percentage represents the average value across all U.S. students. C. Statistic; the percentage represents the calculated average value across all U.S. students. D. Parameter; it is the average for all of the schools that participated in the NSSE.

A. Statistic; it is the mean percentage for the sample of schools that participated in the NSSE, not all schools in the United States.

Suppose that you had calculated the mean, median and mode of the following salary data: $44,751 $52,000 $41,500 $38,862 $51,380 $61,774 How would the mean and the median values be affected if you added an outlier salary of $97,582? A. The outlier would cause a relatively large increase in the mean value, but a smaller increase in the median value. B. The outlier would cause the mean to increase but the median value would be unaffected. C. The outlier would cause a slight increase in the mean and a larger increase in the median value. D. The outlier would cause the both the mean and the median to increase by the same amount.

A. The outlier would cause a relatively large increase in the mean value, but a smaller increase in the median value.

Ability and wages: Arcidiacono, Bayer, and Hizmo (2008) analyzed data from a National Longitudinal Survey called NLSY79, which includes data from over 12,000 men and women in the United States who were in the 14¬ to 22¬year age range in 1979. The researchers reported that ability is related to wages in early career jobs for university graduates, but not for high school graduates. In line with this, research has found that racial discrimination with respect to wages is more prevalent against high school graduates than college graduates, because when ability is not the primary reason for determining wages, other non-relevant factors such as race play in. The researchers suggest that their findings might explain why, on average, a black person is more likely to earn a college degree than is a white person of the same ability level. What do the authors mean by "Longitudinal" in this study? A. This study measured changes in the participants over an extended period of time B. This study had participants that all came from similar parts of the country C. This study had more than two independent variables D. This was a between¬-groups design

A. This study measured changes in the participants over an extended period of time

Frequency tables, histograms, and the Survey of Earned Doctorates: The Survey of Earned Doctorates regularly assesses the numbers and types of doctorates awarded at U.S. universities. It also provides data on the length of time in years that it takes to complete a doctorate. Below is a modified list of this completion-¬time data, truncated to whole numbers and shortened to make your analysis easier. These data have been collected every 5 years since 1982. How would you describe the distribution of these data? 8 8 8 8 8 8 7 6 7 7 7 7 7 6 6 6 6 6 6 7 8 8 8 8 7 6 6 7 7 7 6 11 13 15 15 14 12 9 10 10 9 9 9 A. Unimodal and positively skewed B. Symmetrical with a cluster around 6 to 8 years C. Unimodal and negatively skewed D. Bimodal with peaks at 7 and 15

A. Unimodal and positively skewed

Counts are often converted to percentages. What is 4009 out of 22,140 as a percentage? What type of variable is this data when presented as a percentage? A. 0.18%; scale B. 18.11%; scale C. 5.52%; nominal D. 18.11%; ordinal

B. 18.11%; scale

Type of frequency distribution: Suppose you recorded the finishing times for the nearly 22,000 runners who participate in the Boston Marathon. How would you present these data values when creating a frequency distribution and why? A. Grouped data values because 22,000 values is too many for an individual frequency distribution B. Grouped data values because the range of unique finishing times would be very large C. Individual data values because the values are discrete D. Individual data values because there would be a small range of possible values

B. Grouped data values because the range of unique finishing times would be very large

Developing research ideas from frequency distributions: Below are frequency distributions for two sets of data collected by counting the number of people/friends who appear in the photographs displayed on students' dorm doors and on faculty members' office doors across campus. A. Maybe the images on people on the students doors are not actually friends and family members B. Perhaps the (older) faculty members take fewer pictures at social gatherings, so they are less likely to document friendships through photographs C. The fact that fewer faculty doors were analyzed D. The researchers may have been biased in which doors they looked at

B. Perhaps the (older) faculty members take fewer pictures at social gatherings, so they are less likely to document friendships through photographs

Externalizing behavior, anxiety, and correlation: A study on the relation between rejection and depression in adolescents (Nolan, Flynn, & Garber, 2003) also collected data on externalizing behaviors (e.g., acting out in negative ways, such as causing fights) and anxiety. They wondered whether externalizing behaviors were related to feelings of anxiety. Some of the data are presented in the accompanying table. The Pearson correlation coefficient for this data is 0.65. If you added one more participant who scored 1 on externalizing and 45 on anxiety, the correlation coefficient would change to 0.12. Why does the correlation change so much with the addition of just one participant? A. The value changes because the new data point has a high anxiety score. B. The value changes so much because the new point is an outlier that is both high on anxiety and low on externalizing. C. The value changes because the sum of squares values is altered drastically by adding a new data point. D. The value changes so much because the new data point has a low externalizing score.

B. The value changes so much because the new point is an outlier that is both high on anxiety and low on externalizing.

Which of the following statements accurately describes how to assess the mean both visually and arithmetically? A. Visually, the mean is under the highest point on the histogram; arithmetically, it is the middle score when the data is arranged in ascending order. B. Visually, the mean is the point on a histogram that seems to create balance between the two sides of the data distribution; arithmetically it is the sum of all the data values divided by the total number of scores. C. Visually, the mean is under the highest point on the histogram; arithmetically it is the sum of all the data values divided by the total number of scores. D. Visually, the mean is the point on a histogram that seems to create balance between the two sides of the data distribution; arithmetically, it is the middle score when the data is arranged in ascending order.

B. Visually, the mean is the point on a histogram that seems to create balance between the two sides of the data distribution; arithmetically it is the sum of all the data values divided by the total number of scores.

Calculate the standard deviation of these salary values. $44,751 $52,000 $41,500 $38,862 $51,380 $61,774 A. $48,065.50 B. $48,377.83 C. $7,665.94 D. $22,912

C. $7,665.94

On a test of marital satisfaction, scores could range from 0 to 27. If we wanted to create a frequency table with six intervals, what would the bottom/lower value of each interval be? A. 0, 6, 12, 18, 24, 30 B. 0, 4, 8, 12, 16, 20 C. 0, 5, 10, 15, 20, 25 D. 1, 5, 10, 15, 20, 25

C. 0, 5, 10, 15, 20, 25

Sample versus population in Norway: The Nord¬Trøndelag health study surveyed more than 60,000 people in a Norwegian county and reported that "people who have gastrointestinal symptoms, such as nausea, are more likely to have anxiety disorders or depression than people who do not have such symptoms." What is the population to which the researchers would like to extend their findings? A. All Americans B. The 60,000 individuals they studied C. All Norwegians or possibly all people D. All individuals with anxiety disorders

C. All Norwegians or possibly all people

A researcher studies the average distance that 130 people living in U.S. urban areas walk each week. How might you operationalize the average distance walked in 1 week as an ordinal measure? A. By sorting the people into groups based on gender or ethnicity B. By counting the number of steps each individual took C. By sorting the people into groups such as "long distance walked," "medium distance walked," and "short distance walked" D. By measuring the number of miles walked

C. By sorting the people into groups such as "long distance walked," "medium distance walked," and "short distance walked"

Between¬-groups versus within¬-groups and exercise: Noting marked increases in weight across the population, researchers, nutritionists, and physicians have struggled to find ways to stem the tide of obesity in many Western countries. They have advocated a number of exercise programs, and there has been a flurry of research to determine the effectiveness of these programs. Which of the following research designs would allow you to examine the effects of an exercise program on weight loss in comparison with a program that does not involve exercise using a within¬-groups design? A. Recording each participant's weight and the number of times they exercise per week B. Randomly assigning half the participants to an exercise group and the other half to a non¬exercise group C. Measuring all participants'; weights before starting an exercise program and then again once the program had concluded D. Assigning participants to two groups based on whether or not they exercise regularly, then tracking the average weight of each group

C. Measuring all participants'; weights before starting an exercise program and then again once the program had concluded

Types of variables and the Kentucky Derby: The Kentucky Derby is perhaps the premier event in U.S. horse racing. As racing fans, we would be very interested in the variable of finishing position. For example, a stunning upset took place in 2005 when Giacomo, a horse with 50¬1 odds, won, followed by Closing Argument and then Afleet Alex. What type of variable is finishing position? A. Nominal B. Ratio C. Ordinal D. Interval

C. Ordinal

Measures of central tendency for measures of baseball performance: Here are winning percentages for 11 baseball players for their best 4¬year pitching performances: 0.755 0.721 0.708 0.773 0.782 0.747 0.477 0.817 0.617 0.650 0.651 Calculate and then compare the mean and the median. What does the relationship between the two tell us about the skew of the data? A. The mean and the median do not give us enough information to tell if the data are skewed. B. The mean is lower than the median, so the data are somewhat positively skewed. C. The mean is lower than the median, so the data are somewhat negatively skewed. D. The median is within one standard deviation of the mean, so the data are symmetric.

C. The mean is lower than the median, so the data are somewhat negatively skewed.

Direction of a correlation: Which of the following relationships would you expect to exhibit a positive correlation? A. Direction of a correlation: Which of the following relationships would you expect to exhibit a positive correlation? B. The relationship between time spent studying and questions missed on an exam. C. The relationship between level of education and salary at age 40. D. None of these would be a positive correlation

C. The relationship between level of education and salary at age 40.

Obesity, age at death, and correlation: In a newspaper column, Paul Krugman (2006) mentioned obesity (as measured by body mass index) as a possible correlate of age at death. What is the likely correlation between these variables? A. There is likely to be a small or moderate positive correlation. B. There is likely to be a very strong positive correlation. C. There is likely to be a small or moderate negative correlation. D. There is likely to be a very strong negative correlation.

C. There is likely to be a small or moderate negative correlation.

Frequencies, distributions, and numbers of friends: A college student is interested in how many friends the average person has. She decides to count the number of people who appear in photographs on display in dorm rooms and offices across campus. She collects data on 84 students and 33 faculty members. The data are presented below. A. Unimodal and negatively skewed B. Bimodal and positively skewed C. Unimodal and positively skewed D. Bimodal and negatively skewed

C. Unimodal and positively skewed

Frequencies, distributions, and numbers of friends: A college student is interested in how many friends the average person has. She decides to count the number of people who appear in photographs on display in dorm rooms and offices across campus. She collects data on 84 students and 33 faculty members. The data are presented below.Roughly how many people have more than 18 people pictured? A. 9 B. 91 C. 34 D. 27

D. 27

IQ¬-boosting water and illusory correlation: The trashy tabloid Weekly World News published an article —"Water from Mountain Falls Can Make You a Genius"—stating that drinking water from a special waterfall in a secret location in Switzerland "boosts IQ by 14 points—in the blink of an eye!" (exclamation point in the original). Hans and Inger Thurlemann, two hikers lost in the woods, drank some of the water, noticed an improvement in their thinking, and instantly found their way out of the woods. The more water they drank, the smarter they seemed to get. They credited the "miracle water" with enhancing their IQs. They brought some of the water home to their friends, who also claimed to notice an improvement in their thinking. Which of the following statements expresses a potential problem with the Weekly World News's conclusion? A. The data came from a small, self¬-selected sample. B. The reports of improved intelligence were subjective, not objective or quantitative. C. There is an obvious confounding variable in the Thurlemans' report. D. All of these statements are problems with the conclusion.

D. All of these statements are problems with the conclusion.

Direction of a correlation: Which of the following relationships would you expect to exhibit a negative correlation? A. The relationship between the amount of wine you consume with dinner and your alertness after dinner. B. The relationship between how often you say no to dessert and your body fat level. C.Neither of these would be negative correlations. D. Both of these would be negative correlations.

D. Both of these would be negative correlations.

Romantic relationships: In a 2010 report, Goodman and Greaves (2010) reported findings from an analysis of data from participants in a large research project in the United Kingdom, the Millennium Cohort Study. They stated that ". . . while it is true that cohabiting parents are more likely to split up than married ones, there is very little evidence to suggest that this is due to a causal effect of marriage. Instead, it seems simply that different sorts of people choose to get married and have children, rather than to have children as a cohabiting couple, and that those relationships with the best prospects of lasting are the ones that are most likely to lead to marriage" (p. 1). Is this a correlational study or an experiment? Explain. A. Correlational; the researchers found no evidence for a causal effect. B. Experimental; the researchers were looking for a possible causal effect of marriage. C. Experimental; the participants were divided into two separate groups. D. Correlational; the participants were measured but not randomly assigned to groups

D. Correlational; the participants were measured but not randomly assigned to groups

A study of the effects of skin tone (light, medium, and dark) on the severity of facial wrinkles in middle age might be of interest to cosmetic surgeons. What are the independent and dependent variables in this study? A. Independent variable: skin tone; dependent variable: age B. Independent variable: severity of wrinkles; dependent variable: skin tone C. Independent variable: age; dependent variable: severity of wrinkles D. Independent variable: skin tone; dependent variable: severity of wrinkles

D. Independent variable: skin tone; dependent variable: severity of wrinkles

Types of variables and the Kentucky Derby: The Kentucky Derby is perhaps the premier event in U.S. horse racing. As racing fans, we might be interested in the variable of finishing time. Giacomo won in 2 minutes, 2.75 seconds. What type of variable is finishing time? A. Ordinal B. Nominal C. Interval D. Ratio

D. Ratio

Central tendency and outliers for data on global TV viewing habits: Below are approximate, daily average viewing times for 12 countries based on 2007 data from the Economist Web site (http://www.economist.com/): United States 8.2 hours Turkey 5 hours Italy 4.05 hours Japan 3.75 hours Spain 3.6 hours Portugal 3.5 hours Australia 3.2 hours South Korea 3.16 hours Canada 3.1 hours Britain 3 hours Denmark 3 hours Finland 2.8 hours How would the mean and median values of this data be affected by excluding the United States from the analysis? A. The mean value would be unchanged; the median value would decrease slightly. B. Neither the mean nor the median value would be affected. C. The mean value would decrease; the median would be unchanged. D. The mean value would decrease; the median value would decrease slightly.

D. The mean value would decrease; the median value would decrease slightly.

Mean versus median for temperature data: A visitor's guide to the Mount Washington Observatory details the "normal" daily maximum and minimum temperatures recorded at the Observatory for each month of the year. These values are likely to be measures of central tendency for each month over time. The guide does not say if these "normal" temperatures are mean or median values. Which of the following explanations provides the best reasoning for using one type of statistic over the other? A. The median value should be used because it is the value most people think of as "normal." B. The mean value should be used since it is always the most accurate measure of central tendency. C. The mean value should be used because it factors in very high and very low temperatures. D. The median value should be used because it is less affected by extreme weather days (outliers).

D. The median value should be used because it is less affected by extreme weather days (outliers).