Stat Test 1

When buying a home, the interest rate given on a loan typically depends on the applicant's credit score. The Fair Isaac Corporation (FICO) is a major producer of credit scores. The following table contains 10 randomly selected loan applicants along with their FICO scores and the interest rates that they were given when financing their homes. FICO Score Interest Rate 756 6.32 679 7.85 527 10.2 839 5.52 677 7.3 686 7.37 512 9.67 590 8.4 765 5.82 502 10.01

- 0.9819

An urn contains 23 red marbles, 27 blue marbles, and 40 yellow marbles. One marble is to be chosen from the urn without looking. What is the probability of choosing a red marble? Your answer should be to rounded to 4 decimal places.

0.2556 Feedback Correct! The number of red marbles is 23. The total number of marbles is the sum of the numbers of red, blue, and yellow marbles. 23 + 27 + 40 = 90 23/90 = 0.2556

Consider the following table summarizing the speed limit of a certain road and the number of accidents occurring on that road in January. Posted Speed Limit 55 49 41 35 20 21 Reported Number of Accidents 26 25 20 19 17 14 1) Find the slope of the regression line predicting the number of accidents from the posted speed limit.Round to 3 decimal places. 2) Find the intercept of the regression line predicting the number of accidents from the posted speed limit. Round to 3 decimal places. 3) Predict the number of reported accidents for a posted speed limit of 21mph. Round to the nearest whole number.

1) 0.307 2) 8.856 3) 15

Suppose Joan has a fair four-sided die with sides that are numbered 1, 2, 3, and 4. After she rolls it 37 times, Joan finds that she's rolled the number 3 a total of five times. What is the empirical probability that Joan rolls a 3?

13.51 % Feedback Correct. In five of the 37 different attempts, Joan rolled a 3. So the probability is five / 37 = 13.51 %.

The distribution of IQ (Intelligence Quotient) is approximately normal in shape with a mean of 100 and a standard deviation of 17. According to the standard deviation rule, only ____% of people have an IQ over 117.

16

Here are the number of hours that 9 students spend on the computer on a typical day: 1 2 2 3 6 7 11 12 14 What is the mode number of hours spent on the computer?

2

A study analyzed data from the National Longitudinal Study of Adolescent Health. Participants were followed into adulthood. Each study participant was categorized as to whether they were obese (BMI >30) or not and whether they were dating, cohabiting, or married. The researchers were trying to determine the effect of relationship status on obesity. The table below summarizes the results: Based on the table above, the percentage of Married participants, who were Obese is:

34.9%

A recent survey asks 89 students, How many hours do you spend on the computer in a typical day? Of the 89 respondents, 3 said 1 hour, 3 said 2 hours, 12 said 3 hours, 23 said 4 hours, 19 said 5 hours, 17 said 6 hours, 7 said 7 hours, 4 said 8 hours, 1 said 9 hours. In table format, the results look like this: # hours: 1 2 3 4 5 6 7 8 9 # students: 3 3 12 23 19 17 7 4 1 What is the average (mean) number of hours spent on the computer?

4.8

The distribution of the amount of money spent by students on textbooks in a semester is approximately normal in shape with a mean of: μ= 380 and a standard deviation of: σ= 24. According to the standard deviation rule, almost 2.5% of the students spent more than what amount of money on textbooks in a semester?

428

Based on the results of a nationwide study, the number of contacts programmed into cell phones are summarized on the following boxplot: Which interval contains the greatest amount of data?

50-100 Feedback Correct. This interval stretches from Q1 to well above the median, so we can be sure that it contains more than 25% of the data. No other interval has more than 25% of the data, so this is the best answer.

Look at the table below Score Count [40-50) 2 [50-60) 2 [60-70) 4 [70-80) 3 [80-90) 2 [90-100) 3 What percentage of students earned a grade of less than 90?

81%

The distribution of IQ (Intelligence Quotient) is approximately normal in shape with a mean of 100 and a standard deviation of 19. According to the standard deviation rule, _____% of people have an IQ between 43 and 157. Do not round

99.7

Suppose that P(A) = 0.95. Which of the following is the best interpretation of this statement?

Event A is extremely likely, but in a long sequence of trials, it occasionally will not occur. Feedback Correct. Since P(A) = 0.95 is very close to 1, then event A is extremely likely. In other words, event A will almost always occur, but occasionally, in a long sequence of trials, it will not occur.

The weights (in pounds) and cholesterol levels (in mg/dL) of several individuals was observed. The data are shown in the scatterplot below: The outlier on the graph is likely due to an error in recording the data. Which of the following statements is true?

If the outlier were removed, the correlation coefficient (r) would increase. Feedback Correct. The outlier lies outside the linear pattern formed by most of the data. Since correlation measures how tightly the points in a graph cluster about a straight line, removing the outlier, which has the largest deviation from the line will increase the correlation.

The boxplots below show the number of marshmallows in a bag, as estimated by students in two elementary school classes. Which class has greater variability in students' estimate of the number of marshmallows?

Ms. Apple's class Feedback Correct. The class whose boxplot appears "longer" is the class whose real estate values had more variability. In this case, Ms. Apple's class has more variability, since we see that the boxplot for her class extends more on either side than the boxplot for Ms. Banana's class.

The boxplots below show the number of marshmallows in a bag, as estimated by students in two elementary school classes. Which class has a greater percentage of estimates between 50 and 100 marshmallows?.

Ms. Banana's class Feedback Correct. In fact, the percentage of estimates between 50 and 100 is exactly 50% since this is the percentage of scores between the minimum value (50) and the median (100), while we can reason that less than 50% of Ms. Apple's class gave estimates in this same range.

A student survey was conducted at a major university, and data were collected from a random sample of 750 undergraduate students. One variable that was recorded for each student was the student's answer to the question "With whom do you find it easiest to make friends? Opposite sex/same sex/no difference." These data would be best displayed using which of the following?

Pie Chart

A local ice cream shop kept track of the number of cans of cold soda it sold each day, and the temperature that day, for 2 months during the summer. The data are displayed in the scatterplot below: Which of the following is the best description of the relationship between X and Y as it appears in the scatterplot?

Positive linear relationship with outlier(s) Feedback Correct. The graph displays a positive relationship: an increase in X is associated with an increase in Y. The relationship is linear because it can be described as points scattered about a line. Finally, it has one point that deviates from the pattern of the relationship, which is considered an outlier.

Which of the following is an example of stratified sampling?

Proponents of a local ballot measure conduct a survey of the city by randomly selecting 100 potential voters from each of its 18 zip codes. Feedback Correct. The proponents viewed the voters as being divided into 18 separate strata, and a few voters from each stratum were selected.

Based on the results of a nationwide study, the number of contacts programmed into cell phones are summarized on the following boxplot: Choose the correct label for the point on the boxplot represented by the question mark:

Q3

A study seeks to answer the question, "Does Vitamin C level in the breast milk of new mothers reduce the risk of allergies in their breastfed infants?" The study concluded that high levels of vitamin C (measured in mg) were associated with a 30 percent lower risk of allergies in the infants. In this scenario, "levels of vitamin C (measured in milligrams)" is what type of variable?

Quantitative

The histogram below displays the distribution of 50 ages at death due to trauma (accidents and homicides) that were observed in a certain hospital during a week. Which of the following best describes the shape of the histogram?

Right-skewed with a possible outlier Feedback: Correct. The distribution of ages is skewed right (which is where the "tail" of the distribution is). Also, the largest observation—approximately equal to 90—is a possible high outlier.

Suppose that the correlation r between two quantitative variables was found to be r=0. Which of the following is the best interpretation of this correlation value?

There is no linear relationship between the two variables. Feedback Correct. The correlation coefficient indicates the strength of the linearity of a scatterplot relationship, and a correlation coefficient that is zero indicates no linear relationship. However, that there might still be some other (non-straight-line) kind of relationship.

When conducting a survey, which of the following is the most important reason to use a random sample?

To avoid bias and to get a representative sample

The city council hired three college interns to measure public support for a large parks and recreation initiative in their city. The interns mailed surveys to 500 randomly selected participants in the current public recreation program. They received 150 responses. True or false? Even though the sample is random, it is not representative of the population of interest.

True Feedback Correct. While the selection of subjects was random, subjects were not representative of the population of the city because only participants in the recreation program were included in the sample. Also, there was a large non-response rate.

A researcher wants to determine if preschool attendance is associated with high school graduation for low-income students. She randomly assigns low-income children to two groups; one group will attend preschool program, the second group will not attend preschool. The researcher plans to follow the children in the study for 20 years and observe whether or not they graduate from high school. Which of the following is the response variable in this study?

Whether or not a subject graduates high school

What type of variable is color?

categorical

Given the following summary statistics, determine the regression equation used to predict y from x. sy 4.75 sx 5.02 r 0.41 x 22.41 y 72.58 slope = y-intercept =

slope = 0.39 y-intercept = 63.89

A person must enter a 4 digit code to gain access to his cell phone. He will enter codes until he is successful, however he cannot try more than 3 times or the phone will lock him out. Let S denote a successful attempt and F denote a failed attempt. What is the sample space for this random experiment?

{S, FS, FFS, FFF}