SE I

For the years 1950 - 1980, the number of heart disease death per 100,000 people in the United States was recorded. The regression line below was computed using statistical software package. Which statement is the correct interpretation of the slope? The regression equation: # of deaths = 7387 - 3.63 (year)

(a) The number of heart disease death per 100,000 people has been dropping by an estimated 3.63 deaths per year on average.

For the owner of the Mini Mart in question 37, assume it costs 35 cents to make one cup of coffee. Using the process of charging customers $1 if they get a 1,2,3,4, or 5 on a die and no charge if the die is a 6, what is the expected profit per cup to the owner?

(b) $0.48

A large sample hypothesis test with σ known of a null hypothesis μ = 15 against the alternative hypothesis μ ≠ 15 results in the test statistic value of z = 1.37 is approximately

(b) 0.1707

Those that study child development found a linear regression model for infants that uses age in months to predict height. A sample of 12 babies was randomly selected and the information shown below was generated. The approximate slope of the least squares regression line is

(b) 0.53

At a certain high school, students who take AP Psychology also take AP Statistics. From past records, the probability that a student gets a 5 in AP Psychology is one-fourth. The probability a student gets a 5 on the AP Statistics exam is one-seventh. What is the probability that a student will get at least one 5 when taking both exam I. If the two events are independent? If the students getting a 5 on the AP Statistics exam are a subset of those students getting a 5 on the AP Psychology exam?

(b) 11/28 and 1/7

A researcher interested in the age at which women are having their first child surveyed a simple random sample of 250 women having at least one child and found an approximately Normal distribution with a mean age of 27.7 and a standard deviation of 5.4. According to the empirical rule, approximately 95% of the women had their first child between the ages of

(b) 16.5 and 38.1 years

At a certain high school, a simple random sample was taken asking 52 11th and 12th graders their political affiliation. The following table was established. If a chi-squared test of independence were performed on these data, what would be the corresponding degrees of freedom? 11th Grade 12th Grade Republican 11 5 Democrat 10 15 Independent 5 6

(b) 2

Early studies of probability were conducted by the Italian mathematician Girolamo Cardano (1501-1576). One of the many dice games that Cardano studied was played with 6-sides dice. Each of the six dice had five blank faces and one face with a number. the numbers 1 through 6 appeared on one of the six dice. All six dice were rolled at once, and the payoff to the gambler was based on the sum of the numbers showing on the up faces. What is the expected value of the sum obtained by rolling all 6 dice?

(b) 3.5

In a statistics course, a linear regression equation was compared to predict the final exam based on the score on the first test of the term. The equation was: final score = 25 + 0.7 (first test score). George scored an 80 on the first test. One the final exam George scored an 85. What is the value of his residual?

(b) 4

(#'s 10 and 11) Which distribution has the smallest standard deviation?

(b) B

Which of the following statements about a linear regression model is true? I. The sum of the residuals is always 0. II. If r^2 = 0, the regression line is a horizontal line. III. No pattern in the residual plot is an indication that a nonlinear model will show a better fit to the data than a straight-line regression model.

(b) I and II only

Which of the following are true? I. A simple random sample is any sampling technique where each element of the population has the same chance of being selected. II. A simple random sample where every set of n elements in the population has the same chance of being selected. III. From a population of N = 10, there are 90 equally likely possible sample of size 2 if we are sampling without replacement.

(b) II only

Which of the following is true? I. If the sample size is constant, then reducing the probability of a Type I error will reduce the probability of a Type II error. II. Increased power can be achieved by reducing the Type II error. III. If the p-value of a test is 0.015, the probability that the null hypothesis is true is 0.015.

(b) II only

The level of significance is always

(b) The maximum probability of a type I error.

When two fair die are rolled, what is the probability of getting a sum of 7 given that the first die rolled is an odd number?

(c) 1/6

The scores of a standardized test designed to measure math anxiety are Normally distributed with a mean of 100 and a standard deviation of 10 for a population of first year college students. Which of the following observations would you suspect is an outlier?

(c) 150

Given the data below, in conducting a test of association between gender and grade, what is the expected count for the number of males who earned a grade of B?

(c) 36.8

Those that study child development found a linear regression model for infants that uses age in months to predict height. A sample of 12 babies was randomly selected and the information shown below was generated. About what percent of the observed variation in the height can be explained by the LSLR of height on age?

(c) 69%

The heights of American men aged 18 to 24 are approximately Normal with mean of 68 inches and a standard deviation of 2.5 inches. About 20% of these men are taller than

(c) 70 inches

A student is interested in the effects of different walking styles on heart rate. He decides to use 30 volunteers from his school for his experiment. All 30 participants find their at rest pulse rates. Each participant will walk twice for 10 minutes, once using a fast pace but with no arm movement and again using a fast pace, but with an exaggerated arm movement style. The experimenter throws a coin to determine which style each participant will walk first. All participants get sufficient rest between walks to let their pulse rates return to normal. The students then compare increased pulse rates based on the walk with no arm movement to increased pulse rate base on the walk with exaggerated arm movement for each student.

(c) Blocking is used in this study to reduce the difference in increased pulse rates among individual students.

A statistics student wishes to test the strength of various brands of paper towels. He chooses 5 brands and selects 6 towels from each brand. He numbers them 1-30. He randomly selects a towel and places it in an embroidery hoop. Exactly 10 ml of water and a large water weight are placed in the center of the towel. The time it takes for the towel to break is recorded. In this case, the explanatory variable is

(c) Brand of paper towel

An airline claims that its planes are, on average, less than 8 minutes in landing. The appropriate hypotheses for examining the claim are

(c) Ho: μ = 8 and Ha: μ < 8

You have sampled 25 students to find the mean SAT scores at Morris Knolls High School. A 95% confidence interval for the mean SAT score is 900 to 1100. Which of the following gives a valid interpretation of this interval?

(c) If this procedure were repeated many times, 95% of the resulting confidence intervals would contain the true mean SAT score at Morris Knolls.

Which of the following is more likely to be true of this distribution? (The distribution is skewed right)

(c) Mean = 4 Median = 3.5 Mode = 3

Multiplying each element of the data set by an integer n will have which effect on the mean and the variance?

(c) The mean is multiplies by n and the variance is multiplies by n^2.

A study was done to determine if the method of instruction (either discussion or lecture) depended on the two of the classes being taught. Twenty art classes, 17 math classes, and 25 science classes were observed. The method of instruction, discussion or lecture, was recorded. Which of the following best describes the relationship between method of teaching and type of class?

(c) There appears to be an association since the art class was less likely to use discussion rather than either math or science.

A cup of coffee at a Mini Mart is usually 50 cents. The manager of the store decides to let the customer roll a die. If the die is a 6, the customer gets the cup of coffee for free. If the die is a 1,2,3,4, or 5, the coffee is $1. A customer buys a cup of coffee one a day, five days a week. A statistics class wishes to know the number of cups of coffee which were free to the customer using a simulation. There were 25 students in the class. Each student did 4 simulations. Which frequency table below is most likely to contain the results from these 100 trials

(d)

An inspection procedure at a manufacturing plant involves picking three items at random and then accepting the whole lot if at least two of the three items are in perfect condition. If in reality 80% of the whole lot is perfect, what is the probability that the whole lot will be accepted?

(d) 0.896

You want to estimate the mean SAT score for a population of students with a 90% confidence interval. Assume that the population standard deviation is σ = 100. If you want the margin of error to approximately 10, which of the following would be the desired minimal sample size?

(d) 271

A 90% confidence interval for a population mean is determined to be 800 to 900. If the confidence is increased to 95% confidence which the sample statistics and sample size remain the same, the confidence interval for μ

(d) Becomes wider

Which of the following is true? I. The larger the sample, the smaller the spread in the sampling distribution. II. Provided that the population size is significantly greater than the sample size, the spread of a sampling distribution is about the same no matter what the sample size. III. Sampling distributions from non-normal populations are approximately Normal provided that n is large.

(d) I and III only

Polly takes three standardized tests. She scores 600 on all three. Using standard scores, or z-scores, rank her performance on three tests from best to worst in the means of standard deviations for the tests are as follows: Mean Standard Dev. Test I: 500 80 Test II: 470 120 Test III: 560 30

(d) III, I, II

A student was interested in the relationship between weight of a car and gas consumption measured in mpg. He selected 16 different automobiles and recorded their weights along with their advertised mpg. The regression equation and plot are shown below. What effect would the addition of the point (4300 lbs, 15.63 mpg) have on the value of r^2?

(d) It will increase r^2 because it is an influential point which lies on the lease squares regression line.

For the past two hundred years population per square feet in a northwest suburb can be modeled using the exponential equation: y = ab^x. The scatterplot of the data is shown below. The r^2 value of the exponential model is 0.98. Which of the following statements is true?

(d) Plotting the logarithm of the population per square mile against year should be approximately linear.

The residual plot shown below came from data which plotted grade at midterm against grade on final exam. A linear regression line was calculated. Which conclusion could be reached by analyzing the residual plot?

(d) There exists unequal variance throughout the model.

Suppose the regression line for a set of data ŷ = 3x + b, passes through the point (2,5). If x̅ and Ӯ are the sample means of the x and y values respectively, then ŷ=

(e) 3x̅ - 1

(#'s 10 and 11) In which distribution(s) would you be more likely to find the mean and median the same?

(e) A, B, and C

Which of the following will most likely approximate a uniform distribution?

(e) Ages of students at a particular high school.

A candidate for mayor hires a statistician to determine the amount of support he has for the upcoming election. The statistician tests the null hypothesis that the population proportion equals 50% against the alternative hypothesis that the population proportion is greater than 50%. The results of a simple random sample of 91 registered voters can be found in the printout below. (Print out shows p-value = 0.0044) The conclusion which can be reached is I. The candidate can be quite confident that he has more than 50% of the vote. II. The p-value of 0.0044 tells us that we cannot reject the null hypothesis and that the candidate has 50% or less of the vote. III. The p-value of 0.0044 indicates that it is not very likely to get an observed value of 0.637 and the null hypothesis is true.

(e) I and III

Which statement is true about the box plot shown? I. It is a left skewed distribution which has outliers. II. It is a symmetrical distribution which has outliers. III. The interquartile range is less than one. IV. Approximately 75% of the observations have a GPA less than 3.

(e) I,III, and IV