STA 115 Test 2 Chp. 7, 8, 11, 12, 14 and 15.

Term: Response Variable

A variable that measures an outcome or result of a study.

Term: Explanatory Variable

A variable that we think explains or causes changes in the response variable

At State University, an investigation by the National Collegiate Athletic Association (NCAA) found that 96 student athletes had engaged in some form of illegal gambling activities. At City College, a similar investigation found that 23 student athletes were found to have engaged in illegal gambling activities. 1. What would be a more appropriate measure that would make the comparison fair? 2. Why is it not fair to use these two numbers to conclude that illegal gambling is more of a problem among the student athletes at State University that it is at City College?

1. Compare the percentage of student athletes involved in illegal gambling activities. 2. One school may have more student athletes than the other school has.

You are planning an experiment to determine the effect of the brand of gasoline and the weight of a car on gas mileage measured in miles per gallon. You will use a single test car, adding weights so that its total weight is 3000, 3500, or 4000 pounds. The car will drive on a test track at each weight using each of Exxon, Sunoco, and Texaco gasoline. 1. In this study, gasoline brand is a(n) 2. In this study, gasoline brand and weight is a

1. Explanatory Variable 2. Gasoline brand is a categorial variable and weight is a quantitative variable.

Lean body mass (your weight leaving out fat) helps predict metabolic rate (how many calories of energy you burn in an hour). The relationship is roughly a straight line. The least-squares regression line for predicting metabolic rate (y in calories) from lean body mass (x in kilograms) is y = 113.2 + 26.9x

26.9—that is, when lean body mass goes up by 1 kg, metabolic rate goes up by 26.9 calories.

You gather data on the number of hours of television news broadcasts watched per week and the grade point average of juniors majoring in journalism. You expect that TV news broadcast watching will help explain grades. 1. In a scatterplot of your data, 2. The plot of the data in the preceding question shows that students who watch more TV news broadcast watching tend to have higher grade indexes. You calculate the correlation r between hours of TV and grade point average. A plausible value is

1. hours of TV news broadcast watching should be on the horizontal axis. 2. r = 0.4.

Suppose that the correlation between the scores of students on Exam 1 and Exam 2 in a statistics class is r = 0.7. One way to use r is to compute the percent of the variation in Exam 2 scores can be explained by the straight-line relationship between Exam 2 scores and Exam 1 scores. This percent is about A)7%. B)49%. C)30%. D)84%. E)70%.

49% Note: To turn correlation into a percent is simple, all you need to do is square it.

One of the following 12 scores: 84 76 92 96 88 96 68 80 92 88 76 96, was omitted from the stemplot below: 6 | 8 7 | 66 8 | 0488 9 | 2266

96

Term: Scatterplot

A graph in which the values of two variables are plotted along two axes, the pattern of the resulting points revealing any correlation present.

Term: Histogram

A graphical display where the data is grouped into ranges, and then plotted as bars.

Term: Boxplot

A graphical rendition of statistical data based on the minimum, first quartile, median, third quartile, and maximum. The term "box plot" comes from the fact that the graph looks like a rectangle with lines extending from the top and bottom. Because of the extending lines, this type of graph is sometimes called a box-and-whisker plot.

Term: Lurking Variable

A variable that has an important effect on the relationship among the variables in a study but is not one of the explanatory variable.

The five-number summary for scores on a statistics exam is 11, 35, 61, 70, 79. In all, 380 students took the test. About how many students had scores between 35 and 61? A)95 B)285 C)61 D)35 E)190

A) 95

If a bar graph is to be accurate, it is essential that: A)the bars all have the same width. B)both horizontal and vertical scales be clearly marked in equal units. C)the bars touch each other. D)the explanatory variable be plotted on the horizontal axis. E)the bars be drawn vertically.

A) The bars all have the same width.

The following is a stemplot of 12 exam scores. (The stem is the tens place and the leaf is the ones place.): 6 | 8 7 | 66 8 | 0488 9 | 22666 The first and third quartiles are, respectively, A)78 and 94. B)92 and 76. C)76 and 92. D)94 and 78. E)None of the above

A)78 and 94. Split numbers into quartiles: 68 76. 76. | 80. 84. 88. | 88. 92. 92. | 96 96. 96 80+76= 156/2= 78 92+96= 188/2= 94

The five-number summary for scores on a statistics exam is 11, 35, 61, 70, 79. In all, 380 students took the test.28. With only the above information, which of the following graphs could you draw? A)A boxplot B)A scatterplot C)A stemplot. D)A histogram E)Both a histogram and a boxplot

A)A boxplot

Term: Confounding Variable

An "extra" variable that you didn't account for. They can ruin an experiment and give you useless results. They can suggest there is correlation when in fact there isn't. They can even introduce bias. That's why it's important to know what one is, and how to avoid getting them into your experiment in the first place.

The standard deviation of the numbers 68,979,821 and 68,979,823 is A)not defined. B)the same as the standard deviation of 1 and 3. C)zero. D)very large. E)None of the above

B) The same as the standard deviation of 1 and 3.

Studies with human subjects must be approved in advance by an institutional review board. The board's main purpose is to A)be sure that the study is valid. B)be sure that the subjects of the study are safe. C)be sure that the study is scientifically interesting. D)be sure that the study will have some benefit to society. E)be sure that the study uses good statistical techniques.

B)be sure that the subjects of the study are safe.

To display the percent of adult women who were in the work force in each of the years 1975 to 2000, a good choice of a graph would be a A)stemplot. B)pie chart. C)boxplot. D)line graph. E)histogram.

D) Line Graph because a quantitive variable plots each observation against the time at which it was measured.

The five-number summary for scores on a statistics exam is 11, 35, 61, 70, 79. In all, 380 students took the test. What does the five-number summary suggest about the skewness of the distribution of scores? A)Skewed to the right B)Can not be determined from this information. C)Nothing D)Skewed to the left E)Not skewed

D) Skewed to the left

When repeated measurements each have a systematic error in the same direction, we say that the measurements contain A)measurement error. B)predictive validity. C)random error. D)bias. E)precision.

D)bias

The following is a stemplot of 12 exam scores. (The stem is the tens place and the leaf is the ones place.): 6 | 8 7 | 66 8 | 0488 9 | 22666 The mean is A)greater than the median because the distribution is skewed left. B)less than the median because the distribution is skewed right. C)impossible to determine. D)less than the median because the distribution is skewed left. E)equal to the median.

D)less than the median because the distribution is skewed left.

The five-number summary for scores on a statistics exam is 11, 35, 61, 70, 79. In all, 380 students took the test. For the distribution of 380 exam scores, A)we have no indication of whether the mean is larger than, smaller than, or equal to the median. B)the mean and the median are probably about equal. C)the mean is very likely to be greater than the median. D)the median is very likely to be greater than the mean.

D)the median is very likely to be greater than the mean.

The following is a stemplot of 12 exam scores. (The stem is the tens place and the leaf is the ones place.): 6 | 8 7 | 66 8 | 0488 9 | 22666 The median is A)90. B)84. C)85. D)86. E)88.

E) 88

A study of many countries finds a strong positive correlation between the life expectancy in a country and the percentage of households in the country with telephones. This means that A)life expectancy could be significantly increased by installing more telephones. B)in countries where life expectancy is high, telephone ownership tends to be low. C)in countries where telephone ownership is low, life expectancy tends to be high. D)telephone use is a major contributing cause of longer life. E)None of the above

E) None of the above. No answer correctly describes the relationship between the two observations.

Asking subjects to agree to participate in a study after first informing them of the nature of the study and possible risks and benefits is called

Informed Consent

A researcher creates a machine that will measure the total electrical activity in a human brain over a short period of time. She claims that this measures the intelligence of the brain's owner. A psychologist says that's not true because the amount of electrical activity isn't related to ability to solve problems. The psychologist is claiming that electrical activity as a measure of intelligence is

Invalid because there is nothing to show a correlation between electricity in the brain and one's ability to solve problems. There exist no bias. While it is not precise, it is correct to say that it is invalid. The information isn't not reliable because it hasn't gone to any point where it would be labeled not reliable.

When pictures replace the bars in a graph, the resulting graph is called a?

Pictogram

Term: Categorial Variable

Places an individual into one of several groups or categories.

Term: Quantitative Variable

Takes numerical values for which arithmetic operations such as adding and averaging make sense.

A study of child development measures the age (in months) at which a child begins to talk and also the child's score on an ability test given several years later. The study asks whether the age at which a child talks helps predict the later test score. The least- squares regression line of test score y on age x is y = 110 - 1.3x. According to this regression line, what happens (on the average) when a child starts talking one month later?

The test score goes down 1.3 points

Term: Scatterplot

a graphic tool used to display the relationship between two quantitative variables.

When a line graph displays data after expected seasonal variation has been removed, we say that the data have been: A. variably adjusted B. trend adjusted C. seasonally adjusted D. unbiased E. deviation adjusted

seasonally adjusted

Using this regression line, you predict that a person with lean body mass 50 kilograms will have metabolic rate equal to about how many calories?

y = 113.2 + 26.9x y = 113.2 + 26.9(50) y = 113.2 + 1345 y = 1458.2