Test 2

Consider the following data points: X Y 12 234 13 238 12.5 240 10 500 11 432 9 453 12 123 Use X as the independent variable and Y as the dependent variable. What is the slope of the least squares (best-fit) line? Select one: a. -81.4 b. -45.2 c. 34.6 d. 67.1

a. -81.4

Assume a total of 200 students are represented in the Venn diagram below. 120 of them are part of the football team, and 100 students are part of the soccer team, how many students are on both teams? Select one: a. 20 b. 80 c. 100 d. 120

a. 20

Suppose that at a shopping center with 1,050 shoppers, 550 arrived by car and 120 arrived by bus. Which of the following mathematical operations would result in the probability that a shopper picked from this group at random arrived either by car or bus? Select one: a.5501050+12010505501050+1201050 b.(5501050)×(1201050)(5501050)×(1201050) c.5501050+1201050−(1050−550−120)10505501050+1201050−(1050−550−120)1050 d.(5501050)×(1201050)−(1050−550−120)1050

a. 550/1050+120/1050

Using the t-table, identify the t-value for a 95% confidence interval when the sample size is as small as 11 observations. Select one: a.2.228 b.2.306 c.3.169 d.3.355

a. 2.228

Of the following general derivations, choose the formula that you need for computing a confidence interval for the population mean: Select one: a.Confidence interval = sample mean + margin of error b.Confidence interval = sample mean + standard deviation c.Confidence interval = population mean + margin of error d.Confidence interval = population standard deviation + standard deviation

a. Confidence interval = sample mean + margin of error

Suppose that you have four pieces of fruit in a basket: an orange, an apple, a banana, and a pineapple. You are going to remove a piece of fruit from the basket randomly. What is the probability that you will take an apple from the basket? Select one: a.0.25 b.0.50 c.0.75 d.1.00

a.0.25

What assumption do you need in order to apply the t-distribution? Select one: a.That your random variable is normally distributed. b.That your sample size is large and close to the population size. c.That your sample standard deviation is equal to the population standard deviation. d.That every data point from the sample was chosen at random from the population.

a.That your random variable is normally distributed.

Suppose that the instructor of a math class will give six different versions of the final exam for a large class of 120 students. Each student will receive a version of the final exam determined by a simple roll of a die. With the roll of a fair die, the probability of getting Exam Version 6 is 1/6. This probability is determined using which of the following methods? Select one: a.Repeated sampling b.Equally likely outcomes c.The binomial distribution d.The negative binomial distribution

b.Equally likely outcomes

Using the table below, identify which of the following events is mutually exclusive. Biology Majors Chemistry Majors Total Students First Year Students 120 100 220 Second Year Students 150 150 300 Total Students 270 250 520 Select one: a. All students that are biology and chemistry majors b. First-year students that are biology and chemistry majors c. Chemistry majors that are first-year students and second-year students d. Biology majors that are either first-year students or second-year students

NOT a. All students that are biology and chemistry majors d.Biology majors that are either first-year students or second-year students

What does the Poisson distribution describe? Select one: a.The probability of an event occurring during a fixed time period and/or space. b.The probability of an event occurring during a fixed time period and/or space if this event occurs with a known expected value. c.The probability of a number of events occurring during a fixed time period and/or space if these events occur when these events are dependent on each other. d.The probability of a number of events occurring during a fixed time period and/or space if these events occur with a known average rate and are independent of each other.

NOT a. The probability of an event occurring during a fixed time period and/or space. d.The probability of a number of events occurring during a fixed time period and/or space if these events occur with a known average rate and are independent of each other.

Which of the following describes a method for calculating the sampling distribution of the mean? Select one: a.You compute the mean of a random variable and the standard deviation. b.You take a random sample of data points and plot a histogram of how they deviate from the mean. c.You take a sample of data points and compute their mean, relative frequency, and the box-plot. d.You take a random sample of exam scores and you compute the mean. Then you take another sample with exam scores and compute their mean. Then you take twenty more samples of exam scores and compute their means. You then estimate the probability of each mean.

NOT a.You compute the mean of a random variable and the standard deviation. d.You take a random sample of exam scores and you compute the mean. Then you take another sample with exam scores and compute their mean. Then you take twenty more samples of exam scores and compute their means. You then estimate the probability of each mean.

Identify which of the following statements describes an application of the central limit theorem. Select one: a.You conduct a survey of 10 students at random among 10,000 students at your university. b.You collect the demographic characteristics of all employees at your workplace for Human Resources to analyze later. c.You analyze your average gasoline consumption per week by tracking how many gallons you use on any road trip between 15 and 60 minutes long. d.You use the data from the latest census survey to estimate the average income in City X, which has a population of 3 million people, by selecting 300,000 survey responses at random.

NOT a.You conduct a survey of 10 students at random among 10,000 students at your university. d.You use the data from the latest census survey to estimate the average income in City X, which has a population of 3 million people, by selecting 300,000 survey responses at random.

The error of prediction refers to: Select one: a.how X deviates from Y. b.the mean deviation of X. c.how X and Y behave in a linear way. d.how the observed Y value differs from the predicted Y value.

NOT a.how X deviates from Y. d. how the observed Y value differs from the predicted Y value.

As you increase the sample size from n = 12 to n = 100, which of the following is true? Select one: a.The distribution of the sample mean becomes flatter. b.The distribution of the sample mean becomes uniform. c.The distribution of the sample mean becomes non-normal. d.The distribution of the sample mean becomes more concentrated in the middle.

NOT b.The distribution of the sample mean becomes uniform. NOT a.The distribution of the sample mean becomes flatter. d. The distribution of the sample mean becomes more concentrated in the middle.

What does this formula compute? σest=∑(Y−Y′)^2/N Select one: a.Variance of Y b.Variance of the slope c.Standard deviation of Y d.Standard error of the slope

NOT c.Standard deviation of Y d.Standard error of the slope

Which of the following applies to a continuous probability density function? Select one: a.The probability that you will pass four out of your five final exams. b.The probability that you will miss 30 out of 100 questions on a final exam. c.The probability that you will get a score of 79 points or higher on a final exam. d.The probability that your final exam will contain 100 multiple choice questions where the probability of answering each incorrectly is 0.20.

NOT d.The probability that your final exam will contain 100 multiple choice questions where the probability of answering each incorrectly is 0.20. NOT a.The probability that you will pass four out of your five final exams. c.The probability that you will get a score of 79 points or higher on a final exam.

Suppose that the height of your dog is 1 foot 3 inches and is at the 82nd percentile of all dogs in your neighborhood, then this means that 82% of all dogs in your neighborhood have a height that is ____ 1 foot 3 inches. Select one: a.equal to b.less than c.less than or equal to d.more than or equal to

NOT d.more than or equal to c.less than or equal to

Suppose that you want to test a null hypothesis that states that Math and Chemistry majors do not display any difference in their grades in college-level English literature courses. If you reject that hypothesis when, in actuality, it is true, you will have made which type of error? Select one: a.Type I error b.Type II error c.Standard error d.Sampling error

a.Type I error

In the simple linear regression model, Y = a + bX, the b value is called the: Select one: a.slope. b.constant. c.predictor. d.standard error.

a.slope

Using the table below, compute the correlation coefficient. X 20 21 22 23 24 25 26 Y 100 98 99 101 99 98 97 Select one: a. -0.9793 b. -0.5162 c. 0.5162 d. 0.9793

b. -0.5162

Which of the columns in the table below lists a frequency statistic? Column 1 Column 2 Column 3 Column 4 Savings account money type Number of people with this type of account Bank name Savings as a percent of total money held at that bank, where total = savings + checking US Dollars 1200 Chase 30% European Euro 1800 Bank of America 40% Japanese Yen 2000 Bank of Japan 100% Select one: a. Column 1 b. Column 2 c. Column 3 d. Column 4

b. Column 2

Suppose that a pharmaceutical company makes the assertion that Drug A has a stronger effect than Drug B. To test this claim, 1000 randomly selected people were given the two drugs during different treatment periods. Among them, 600 preferred taking Drug A because of the stronger effect they felt; whereas 400 preferred Drug B. Determine whether there is sufficient evidence, at the 5% level of significance, to support the company's claim that Drug A is stronger and preferred by more than 50% of patients. Select one: a.Reject H0; Drug A is stronger and preferred by less than 50% of patients. b.Reject H0; Drug A is stronger and preferred by more than 50% of patients. c.Do not reject H0; Drug A is stronger and preferred by less than 50% of patients. d.Do not reject H0; Drug A is stronger and preferred by more than 50% of patients.

b. Reject H0; Drug A is stronger and preferred by more than 50% of patients.

If the 95% confidence interval for a slope is upper = 4.55, lower = 2.32, what is your conclusion about the test of the slope? Select one: a.You conclude that there is no linear relationship between X and Y. b.You conclude that there is a positive linear relationship between X and Y. c.You conclude that there is a negative linear relationship between X and Y. d.You conclude that there is a parabolic relationship between X and Y.

b. You conclude that there is a positive linear relationship between X and Y.

Applying the Central Limit Theorem, suppose that personal computers (PC) have a mean of weight of 7.5 pounds with a standard deviation of 1.1 pounds. If you take a sample of the weight of 50 different brands of PC, the sample standard deviation is: Select one: a.7.51.17.51.1 b.1.1√50 c.7.5+1.17.5+1.1 d.7.550√

b.1.1/√50

Suppose that the average weight of a dog is 84 pounds with a standard deviation of 4 pounds. Calculate the z-score for a dog that weighs 90 pounds, assuming that the weight of dogs is normally distributed. Select one: a.1.00 b.1.50 c.2.00 d.2.50

b.1.50 z= (90-84)/4

Compute the expected exam score from passing an exam with 10 true-or-false questions where the probability of answering correctly is 0.70 Select one: a.10 - 7 = 3 b.10 x 0.70 = 7 c.0.7 / 10 = 0.07 d.0.70 x 0.30 = 0.21

b.10 x 0.70 = 7

If a sample mean is normally distributed, a sample size of at least ____ is recommended for applications of the Central Limit Theorem. Select one: a.5 b.30 c.200 d.1000

b.30

Suppose that you want to test the linear relationship between X and Y where you have a sample of 50. For testing such a relationship, the degrees of freedom are: Select one: a.47 b.48 c.52 d.53

b.48

Choose the statement that is true. Select one: a.A correlation coefficient of 1 means that X and Y are not related. b.A correlation coefficient of 0.5994 means that X and Y are strongly positively related. c.A correlation coefficient of -0.8732 means that X and Y are strongly positively related. d.A correlation coefficient of -0.00023 means that X and Y are strongly negatively related.

b.A correlation coefficient of 0.5994 means that X and Y are strongly positively related.

Let x be a random variable that has a normal distribution and represents the number of cars involved in an accident per day. Suppose that you are a researcher and want to determine whether there is sufficient evidence in a sample, at the 1% level of significance, to conclude that the average number of accidents per day is less than 150. Suppose that you gather a sample of 100 days and find that the average number of car accidents is 180 with a standard deviation of 12. What conclusion do you make from your test? Select one: a.Reject H0; the average number of cars is less than 150. b.Reject H0; the average number of cars is more than 150. c.Do not reject H0; the average number of cars is less than 150. d.Do not reject H0; the average number of cars is more than 150.

b.Reject H0; the average number of cars is more than 150.

Identify the type of error in hypothesis testing when the null hypothesis is false but we fail to reject it. Select one: a.Type I error b.Type II error c.Sampling error d.Standard error

b.Type II error

Descriptive statistics may be best defined as the use of: Select one: a.graphics for depicting data. b.methods for summarizing data. c.mathematical models for analyzing data. d.patterns in the data for business decisions.

b.methods for summarizing data.

Which of the following statements is true concerning the correlation coefficient, r? Select one: a.A positive value of r means that when X increases, Y tends to increase and when X decreases, Y tends to increase. b.A positive value of r means that when X decreases, Y tends to decrease and when X increases, Y tends to decrease. c.A negative value of r means that when X increases, Y tends to decrease and when X decreases, Y tends to increase. d.A negative value of r means that when X increases, Y tends to decrease and when X decreases, Y tends to decrease.

c.A negative value of r means that when X increases, Y tends to decrease and when X decreases, Y tends to increase.

ORDERED DATASET:1.002.403.604.454.505.566.897.338.9910.00 Using this ordered dataset, which of the following represents the mode, if it exists? Select one: a.1.00 b.10.00 c.No mode d.1.00 and 10.00

c.No mode

Which of the following represents the use of the discrete probability distribution function? Select one: a.The probability that you spend $45 or less on gasoline this week. b.The probability that the temperature will be above 70 degrees tomorrow. c.The probability that you choose 20 people out of 100 that are unemployed. d.The probability that a person from the population weighs more than 150 pounds.

c.The probability that you choose 20 people out of 100 that are unemployed.

The range is equal to the: Select one: a.middle value of an ordered dataset. b.lowest value plus the highest value. c.highest value minus the lowest value. d.average of the lowest and the highest values.

c.highest value minus the lowest value.

Using the Central Limit Theorem, calculate the 95% confidence interval for the population proportion of people that wear eyeglasses with a sample of size 59 people, of which 15 individuals wear eyeglasses. Assume that the variable of interest in normally distributed. Select one: a.0.2542±1.96×(0.254259)0.2542±1.96×(0.254259) b.0.2542±1.96×0.254259−−−−−√0.2542±1.96×0.254259 c.0.2542±1.96×(0.2542)(1−0.2542)590.2542±1.96×(0.2542)(1−0.2542)59 d.0.2542±1.96×sqrt (0.2542)(1−0.2542)/59

d

Compute the range of the predicted Y value when you have the following information: Y = 2.34 - 12.4X, where X = 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 Select one: a.(-5.28, -100.14) b.(-0, -12.4) c.(1.23, - 10.06) d.(2.34, -121.66)

d. (2.34, -121.66)

What is the difference between a histogram and boxplot? Select one: a.A boxplot is used for quantitative data, whereas a histogram is used for qualitative data. b.A histogram shows the range in the dataset, whereas a boxplot shows only the inner quartile range. c.A histogram shows the values of all observations in the dataset, whereas a boxplot gives the data for only the maximum, minimum, and three inner quartile values. d.A boxplot shows the distribution of the data by plotting the maximum, minimum, and three inner quartiles, whereas a histogram shows how the data is distributed by giving the relative frequency of each interval.

d. A boxplot shows the distribution of the data by plotting the maximum, minimum, and three inner quartiles, whereas a histogram shows how the data is distributed by giving the relative frequency of each interval.

As the sample size increases, the t-distribution: Select one: a.gets flatter. b.becomes bimodal. c.becomes less symmetric. d.experiences larger degrees of freedom.

d. experiences larger degrees of freedom.

The correlation coefficient value is between: Select one: a.0.0 and 1.00 b.-1.00 and 0.00 c.-0.99 and 0.99 d.-1.00 and 1.00

d.-1.00 and 1.00

How many ways can a student select two distinct food items from the cafeteria with ten food items? Select one: a.5 b.20 c.25 d.45

d.45

Which of the following is true concerning the efficiency of an estimator? Select one: a.If the estimator follows a normal distribution, then the expected value of the estimator equals the true parameter value making the bias of the estimator close to 0. b.If the estimator follows a uniform distribution, then the expected value of the estimator equals the true parameter value, thus making the bias of the estimator close to 0. c.If the estimator follows a normal distribution, then the expected value of the estimator approximates the true parameter value, thus making the bias of the estimator close to 0. d.If the estimator is unbiased and follows a normal distribution, then the expected value of the estimator equals the true parameter value, thus making the bias of the estimator equal to 0.

d.If the estimator is unbiased and follows a normal distribution, then the expected value of the estimator equals the true parameter value, thus making the bias of the estimator equal to 0.

Which of the following statements best describes the Central Limit Theorem? Select one: a.The distribution of a random, independent event follows a normal distribution. b.A normally distributed event is independent of other non-normally distributed events. c.It is a process for calculating the relative frequency distribution of a random, independent event. d.It states that given a large sample size, the sampling distribution of the mean of any independent, random variable is normal or nearly normal.

d.It states that given a large sample size, the sampling distribution of the mean of any independent, random variable is normal or nearly normal.

Which of the following is the method for computing the expected value of a discrete random variable? Select one: a.Add the probabilities of each possible outcome. b.Add the probabilities of the mean of each outcome. c.Multiply the probabilities of each outcome by each other. d.Multiply each outcome by its probability and add the results together.

d.Multiply each outcome by its probability and add the results together.

If the expected value from winning a prize when you buy five game tickets this month is $500, then this means that: Select one: a.Your chance of winning is 1 in 5. b.You have an 0.20 probability of winning $500. c.You will win $500 from at least one of those five tickets. d.On average, your winnings from buying five game tickets is $500.

d.On average, your winnings from buying five game tickets is $500.

In a regression model, one of the assumptions is of Homoscedasticity. Which of the following defines Homoscedasticity? Select one: a.The X and Y variables are linearly related. b.The X and Y variables are uniformly distributed. c.The errors of prediction are distributed normally. d.The error terms have the same variance around the regression line.

d.The error terms have the same variance around the regression line.

Identify a one-tail hypothesis test from the statements given below: Select one: a.You want to test if the average household in your city has five residents. b.You want to test if the average weight is equal among male and female cats. c.You want to compare the average income between western and eastern European countries. d.You want to test if the average student in a biology class gets a score of 80% or less on an exam.

d.You want to test if the average student in a biology class gets a score of 80% or less on an exam.

An assumption of the regression model is that: Select one: a.X and Y are independent of each other. b.the values of X are normally distributed. c.the standard deviation of Y is normally distributed. d.the standard error of the slope is normally distributed.

d.the standard error of the slope is normally distributed.