Statistics Chapter 9-10

In the first-order linear regression model, the population parameters of the y-intercept and the slope are estimated by:

b0 and b1

Match the following sample correlation coefficients with the explanation of what that correlation coefficient means. Type the correct letter in each box.

1. r=1, a perfect positive relationship between x and y 2. r=0, no relationship between x and y 3. r= .1, a weak positive relationship between x and y 4. r= -1, a perfect negative relationship between x and y

The regression line is the straight line that bests fits a set of data points according to what?

Least-squares criterion

Can one predict a student's score on the midterm exam in a statistics course from the number of hours the student spent studying for the exam? To explore this, the teacher of the course asks students how many hours they spent studying for the exam and then makes a scatterplot of the time students spent studying and their scores on the exam. In making the scatterplot, the teacher should

plot time spent studying for the exam on the horizontal axis

The best estimator of the difference between two population means μ1−μ2 is the difference between two sample means x¯1−x¯2

true

For a biology project, you measure the weight in grams and the tail length in millimeters of a group of mice. The correlation is r = 0.9. If you had measured tail length in centimeters instead of millimeters, what would be the correlation? (There are 10 millimeters in a centimeter.)

0.9

In regression analysis, if the coefficient of determination is 1.0, then:

the sum of squares for error must be 0

The ratio of two independent chi-squared variables divided by their degrees of freedom is:

F-distributed

In testing for the equality of two population variances, when the populations are normally distributed, the 5% level of significance is used. To determine the rejection region, it is necessary to refer to the F−table corresponding to an upper-tail area of 0.05

false

A regression analysis between weight (y in pounds) and height (x in inches) resulted in the following least squares line: y^=120+5x. This implies that if the height is increased by 1 inch, the weight is expected to:

increase by 5 pounds

In a scatterplot of the average price of a barrel of oil and the average retail price of a gallon of gasoline, you expect to see

a positive association

In testing the difference between two population means using two independent samples, the sampling distribution of the sample mean difference x¯1−x¯2 is normal if the sample sizes are both greater than 30

false

In regression analysis, if the coefficient of correlation is -1.0, then:

the sum of squares for regression and total variation in y are equal.

The linear correlation coefficient of a set of data points is -0.8 a) Is the slope of the regression line positive or negative? b) Determine the coefficient of determination

a) negative b) 0.64

A researcher observes that, on average, the number of divorces in cities with major league baseball teams is larger than in cities without major league baseball teams. The most plausible explanation for this observed association is

the association is due to the presence of a lurking variable (major league teams tend to be in large cities with more people, hence a greater number of divorces)

Does mandatory gun ownership prevent crime? To study this, the number of burglaries committed each month in a small town were recorded for 75 months prior to passage of a bill requiring citizens to own guns and for 56 months after passage of the bill. The goal was to see if the number of burglaries committed was affected by requiring citizens to own guns. The response variable here is

the number of burglaries committed

The expected value of the difference of two sample means equals the difference of the corresponding population means:

the statement is correct under all circumstances

A gambler conducts a study to determine whether the time it took a horse to run its last race can be used to predict the time it takes the horse to run its next race. In this study, the explanatory variable is

the time it took a horse to run its last race

If the coefficient of correlation between x and y is close to 1, this indicates that:

there may or may not be any causal relationship between x and y

In comparing two means when samples are dependent, the variable under consideration is x¯D, where the subscript D refers to the difference

true

In the simple linear regression model, the slope represents the:

change in y per unit change in x

A study found a correlation of r = -0.61 between the gender of a worker and his or her income. You may correctly conclude

this is incorrect because r makes no sense here

For the equation y=6.5x−1, a) the y-intercept is, and the slope is b) the line

a) -1 and 6.5 b) slopes upward

What are all the values that a correlation r can possibly take?

-1 ≤ r ≤ 1

When possible, the best way to establish that an observed association is the result of a cause-and-effect relation is by means of

a well designed experiment

If the coefficient of determination is 0.975, then the slope of the regression line:

could be either positive or negative

The owner of a chain of supermarkets notices that there is a positive correlation between the sales of beer and the sales of ice cream over the course of the previous year. Seasons when sales of beer were above average, sales of ice cream also tended to be above average. Likewise, during seasons when sales of beer were below average, sales of ice cream also tended to be below average. Which of the following would be a valid conclusion from these facts?

The sale of beer and ice cream may both be affected by another variable such as the outside temperature

Regarding linear equations with one independent variable: Which is the general form of such an equation: y=b0+b1x regarding equation above... a) The letter b0 is b) The letter b1 is c) The letter x is d) The letter y is

a) a constant b) a constant c) the independent variable d) the dependent variable

Consider the linear equation y=b0+b1x a) In the equation, b0 is b) In the equation, b1 is c) Give the geometric interpretation of b0. It indicates d) Give the geometric interpretation of b1. It indicates

a) the y-intercept b) the slope c) the y-value where the straight-line graph of the linear equation intersects the y-axis d) how much the y-value on the straight line changes when the x-value increases by unit

Given the least squares regression line y^=−2.48+1.63x, and a coefficient of determination of 0.81, the coefficient of correlation is:

0.90

Industry Research polled teenagers on sunscreen use. The survey revealed that 46% of teenage girls and 30% of teenage boys regularly use sunscreen before going out in the sun. a) identify the two populations b) identify the specified attribute c) are the proportions 0.46 (46%) and 0.30 (30%) population proportions or a sample proportions?

a) teenage girls and teenage boys b) uses sunscreen before going out in the sun c) sample proportions

If the correlation between two variables is close to 0, you can conclude that a scatterplot would show

no straight-line pattern, but there might be a strong pattern of another form