Stats 110 Final - Fall Semester 2019

The average class size this semester in the business school of a particular university is 39.1 students with a standard deviation of 13.6 students. The z-score for a class with 16 students is the closest to ________. A) -1.70 B) 0 C) 1.14 D) 0.43

A) -1.70

A company decided to test the hypothesis that the average time a company's employees are spending to check their private e-mails at work is more than 8 minutes. A random sample of 60 employees were selected and they averaged 8.6 minutes. It is believed that the population standard deviation is 2.3 minutes. The α is set to 0.05. The p-value for this hypothesis test would be ________. A) 0.0220 B) 0.0734 C) 0.0340 D) 0.0480

A) 0.0220

Consider the following cumulative distribution function for the discrete random variable X. x 1 2 3 4 P(X ≤ x) 0.30 0.44 0.72 1.00 What is the probability that X equals 2? A) 0.14 B) 0.56 C) 0.30 D) 0.44

A) 0.14

A random sample of size 100 is taken from a population described by the proportion p = 0.60. Use an appropriate normal transformation to calculate the probability that the sample proportion is less than 0.55. A) 0.1539 B) 0.3669 C) 0.6331 D) 0.8461

A) 0.1539

Let the time between two consecutive arrivals at a grocery store checkout line be exponentially distributed with a mean of four minutes. Find the probability that the next arrival does not occur until at least two minutes have passed since the last arrival. A) 0.6065 B) 0.8153 C) 0.7364 D) 0.0000

A) 0.6065

The following data represent scores on a pop quiz in a business statistics section. 33 68 74 88 78 45 54 64 35 89 64 57 90 23 25 67 68 47 39 26 Suppose the data on quiz scores will be grouped into five classes. The width of the classes for a frequency distribution or histogram is the closest to ________. A) 14 B) 10 C) 12 D) 16

A) 14

A researcher in campaign finance law wants to estimate the proportion of elementary, middle, and high school teachers who contributed to a candidate during a recent election cycle. Given that no prior estimate of the population proportion is available, what is the minimum sample size such that the margin of error is no more than 0.02 for a 99% confidence interval? A) 4147 B) 751.67 C) 752 D) 4160.11

A) 4147

A poker-dealing machine deals spades (1), hearts (2), clubs (3), and diamonds (4) at random as if they were from an infinite deck. In a randomness check, 1600 cards were dealt and counted. The results are shown below. Suit Observed Spades 375 Hearts 395 Clubs 390 Diamonds 440 For the goodness-of-fit test, the value of the test statistic is ________. A) 5.875 B) 5 C) 10.565 D) 9.2

A) 5.875

A sociologist wishes to study the relationship between happiness and age. He interviews 24 individuals and collects data on age and happiness, measured on a scale from 0 to 100. He estimates the following model: Happiness = β0 + β1Age + ε. The following table summarizes a portion of the regression results. Coefficients Standard Error t-stat p-value Intercept 56.1733 5.2169 10.7676 0 Age 0.2867 0.092 3.1163 0.002 The estimate of Happiness for a person who is 82 years old is the closest to ________ A) 80 B) 73 C) 67 D) 83

A) 80

The following frequency distribution shows the frequency of the asking price, in thousands of dollars, for current homes on the market in a particular city. Asking Price Frequency $350 up to $400 5 $400 up to $450 6 $450 up to $500 12 $500 up to $550 7 $550 up to $600 3 What percentage of houses has an asking price under $550,000? A) 90.91% B) 52.31% C) 96.81% D) 70.91%

A) 90.91%

In inferential statistics, we calculate statistics of sample data to A) Both answer choices are correct. B) estimate unknown population parameters. C) conduct hypotheses tests about unknown population parameters. D) Neither answer choice is correct.

A) Both answer choices are correct.

It is known that the length of a certain product X is normally distributed with µ = 36 inches and σ = 4 inches. How is the probability P(X > 44) related to P(X < 32)? A) P(X >44) is smaller than P(X <32). B) P(X >44) is greater than P(X <32). C) P(X >44) is the same as P(X <32). D) No comparison can be made with the given information.

A) P(X >44) is smaller than P(X <32).

Assume the sample space S = {five, six}. Select the choice that fulfills the requirements of the definition of probability. A) P({five}) = 0.7, P({six}) = 0.3 B) P({five}) = 0.7, P({six}) = 0.2 C) P({five}) = 0.7, P({six}) = -0.3 D) P({five}) = 1.0, P({six}) = 0.1

A) P({five}) = 0.7, P({six}) = 0.3

Dr. El-Saidi collected data on the number of hours spent by his 100 students over the weekend to prepare for Monday's Business Statistics exam. He processed the data by Excel and the following incomplete output is available. Mean 18 Sample Variance 7.11 Skewness 1.05 The median is most likely to be ________. A) less than 18 hours B) about 18 hours C) greater than 18 hours D) Cannot be determined from the information provided

A) less than 18 hours

A new sales training program has been instituted at a rent-to-own company. Prior to the training, six employees were tested on their knowledge of products offered by the company. Once the training was completed, the employees were tested again in an effort to determine whether the training program was effective. Scores are known to be normally distributed. The sample scores on the tests are listed next. Use pretest score as µ1 for population 1 and posttest score as µ2 for population 2, or µD as the difference calculated as pretest score minus posttest score. Pretest Score Posttest Score 56 66 94 97 90 96 69 78 96 90 71 75 Which of the following is the value of the appropriate test statistic? A) t5 = -1.8459 B) z = 1.8459 C) t5 = 1.8459 D) z = -1.8459

A) t5 = -1.8459

The Boston public school district has had difficulty maintaining on-time bus service for its students. Suppose the district develops a new bus schedule to help combat chronic lateness on a particularly woeful route. Historically, the bus service on the route has been, on average, 12 minutes late. After the schedule adjustment, the first 36 runs were an average of eight minutes late. As a result, the Boston public school district claimed that the schedule adjustment was an improvement—students were not as late. Assume a population standard deviation for bus arrival time of 12 minutes.Calculate the value of the test statistic. A) z = −2.00 B) t35 = −0.33 C) z = −0.33 D) t35 = −2.00

A) z = −2.00

James, a production manager, is trying to improve the efficiency of his assembly line. He knows that the machine is set up correctly only 80% of the time. He also knows that if the machine is set up correctly, it will produce good parts 92% of the time, but if set up incorrectly, it will produce good parts only 50% of the time. James starts the machine and produces one part before he begins the production run. He finds the first part to be good. What is the revised probability that the machine was set up correctly? A) 88.00% B) 15.30% C) 40.60% D) 73.60%

A)88.00%

A random sample of size 36 is taken from a population with mean µ = 10 and standard deviation σ = 2. What is the probability that the sample mean is greater than 11? A) 0.4101 B) 0.0013 C) 0.2751 D) 0.6839

B) 0.0013

The labor force participation rate is the number of people in the labor force divided by the number of people in the country who are of working age and not institutionalized. The BLS reported in February 2012 that the labor force participation rate in the United States was 63.7%. A marketing company asks 120 working-age people if they either have a job or are looking for a job, or, in other words, whether they are in the labor force. Use an appropriate normal transformation to calculate the probability that fewer than 60% of those surveyed are members of the labor force. A) 0.8400 B) 0.2005 C) 0.9706 D) 0.7995

B) 0.2005

Consider the following discrete probability distribution. x -10 0 10 20 P(X = x) 0.35 0.19 0.19 0.27 What is the probability that X is greater than 0? A) 0.35 B) 0.46 C) 0.56 D) 0.19

B) 0.46

The time for a professor to grade a student's homework in statistics is normally distributed with a mean of 11.8 minutes and a standard deviation of 2.0 minutes. What is the probability that randomly selected homework will require less than 16 minutes to grade? A) 0.6600 B) 0.9821 C) 0.8424 D) 0.2091

B) 0.9821

The following table shows the distribution of employees in an organization. Martha Foreman, an analyst, wants to see if race has a bearing on the position a person holds with this company. Seniority Race Coordinator Analyst Manager Director White 27 10 15 6 Black 30 12 35 8 Hispanic 27 6 20 11 Asian 17 19 15 4 Assuming that race and seniority are independent, which of the following is the expected frequency of Asian directors? A) 6.42 B) 6.09 C) 0 D) 7.08

B) 6.09

Automobiles traveling on a road with a posted speed limit of 65 miles per hour are checked for speed by a state police radar system. The following table is a frequency distribution of speeds. Speed (miles per hour) Frequency 45 up to 55 52 55 up to 65 327 65 up to 75 269 75 up to 85 20 How many of the cars travelled less than 75 miles per hour? A) 673 B) 648 C) 273 D) 323

B) 648

Automobiles traveling on a road with a posted speed limit of 65 miles per hour are checked for speed by a state police radar system. The following table is a frequency distribution of speeds. Speed (miles per hour) Frequency 45 up to 55 50 55 up to 65 325 65 up to 75 275 75 up to 85 25 How many of the cars travelled less than 75 miles per hour? A) 325 B) 650 C) 275 D) 675

B) 650

The accompanying relative frequency distribution represents the last year car sales for the sales force at Kelly's Mega Used Car Center. Car Sales Relative Frequency 35 up to 45 0.07 45 up to 55 0.15 55 up to 65 0.31 65 up to 75 0.22 75 up to 85 0.25 If Kelly's employs 100 salespeople, how many of these salespeople have sold at least 35 but fewer than 45 cars in the last year? A) 10 B) 7 C) 5 D) 15

B) 7

The director of graduate admissions in a state college is analyzing the relationship between scores in the GRE and student performance in graduate school, as measured by a student's GPA. The table below shows a sample of 10 students. GRE 1230 1630 90 1130 1350 1240 1060 440 980 1060 GPA 3.3 2.6 1.9 3.3 2.6 2.3 3.7 1.9 3.8 3.6 Which of the following statements is correct? A) The correlation coefficient between GRE and GPA is negative and weak; namely it is −0.730. B) The correlation coefficient between GRE and GPA is positive and strong; namely it is 0.426. C) The correlation coefficient between GRE and GPA is negative and strong; namely it is −782. D) The correlation coefficient between GRE and GPA is positive and weak; namely it is 138.667.

B) The correlation coefficient between GRE and GPA is positive and strong; namely it is 0.426.

Data of the stock price for Google was collected at the end of the past four quarters. Which of the following types of data best describe these values? A) Cross-sectional B) Time series C) Nominal D) Ordinal

B) Time series

A car dealer who sells only late-model luxury cars recently hired a new salesperson and believes that this salesperson is selling at lower markups. He knows that the long-run average markup in his lot is $5400. He takes a random sample of 16 of the new salesperson's sales and finds an average markup of $4800 and a standard deviation of $790. Assume the markups are normally distributed. What is the value of an appropriate test statistic for the car dealer to use to test his claim? A) z = −0.75 B) t15 = −3.04 C) t15 = −0.75 D) z = −3.04

B) t15 = −3.04

An analyst is forecasting net income for Excellence Corporation for the next fiscal year. Her low-end estimate of net income is $246,000, and her high-end estimate is $331,000. Prior research allows her to assume that net income follows a continuous uniform distribution. The probability that net income will be greater than or equal to $318,500 is ________. A) 0.897 B) 0.947 C) 0.147 D) 0.272

C) 0.147

A key metric in the cell phone industry is average revenue per user (ARPU), which represents the average dollar amount that a customer spends per store visit. In 2011, AT&T reported their ARPU as $63.56. Suppose the standard deviation for this population is $21.2. What is the probability that the ARPU will be between $60 and $63 from a random sample of 46 customers? A) 0.1271 B) 0.4286 C) 0.3015 D) 0.5879

C) 0.3015

Susan has been on a bowling team for 13 years. After examining all of her scores over that period of time, she finds that they follow a normal distribution. Her average score is 229, with a standard deviation of 18. Using an appropriate normal transformation, what is the probability that in a one-game playoff, her score is more than 234? A) 0.6817 B) 0.5089 C) 0.3897 D) 0.2169

C) 0.3897

The 150 residents of the town of Wonderland were asked their age and whether they preferred vanilla, chocolate, or swirled frozen yogurt. The results are displayed next. Age Preference Chocolate Vanilla Swirl Under 25 years old 37 28 10 18 31 26 At least 25 years old What is the probability a randomly selected customer prefers swirled yogurt or is at least 25 years old? A) 0.17 B) 0.07 C) 0.57 D) 0.87

C) 0.57

It is known that 10% of the calculators shipped from a particular factory are defective. What is the probability that no more than one in a random sample of four calculators is defective? A) 0.2916 B) 0.3439 C) 0.9477 D) 0.6561

C) 0.9477

As of September 30, 2017 the earnings per share (EPS) of five firms in the biotechnology industry are 1.56 2.32 1.94 1.77 0.07 The sample mean and the sample standard deviation are the closest to ________. A) 1.53 and 0.75 B) 1.69 and 0.77 C) 1.53 and 0.86 D) 1.69 and 0.86

C) 1.53 and 0.86

A nursery sells trees of different types and heights. These trees average 60 inches in height with a standard deviation of 21 inches. Suppose that 60 pine trees are sold for planting at City Hall. What is the standard deviation for the sample mean? A) 9.5239 B) 4.2769 C) 2.7111 D) 21

C) 2.7111

Consider the following competing hypotheses: Ho: µ = 0, HA: µ ≠ 0. The value of the test statistic is z = −1.46. If we choose a 1% significance level, what is the correct decision and conclusion? A) Reject the null hypothesis; we can conclude that the population mean is significantly different from zero. B) Reject the null hypothesis; we cannot conclude that the population mean is significantly different from zero. C) Do not reject the null hypothesis; we cannot conclude that the population mean is significantly different from zero. D) Do not reject the null hypothesis; we can conclude that the population mean is significantly different from zero.

C) Do not reject the null hypothesis; we cannot conclude that the population mean is significantly different from zero.

Which of the following is an example of time series data? A) Starting salaries of recent business graduates at Penn State University B) The sale prices of townhouses sold last year C) The monthly sales of cars at a dealership in 2018 D) Results of market research testing consumer preferences for soda

C) The monthly sales of cars at a dealership in 2018

A 7,000-seat theater is interested in determining whether there is a difference in attendance between shows on Tuesday evening and those on Wednesday evening. Two independent samples of 20 weeks are collected for Tuesday and Wednesday. The mean attendance on Tuesday evening is calculated as 5440, while the mean attendance on Wednesday evening is calculated as 5950. The known population standard deviation for attendance on Tuesday evening is 630 and the known population standard deviation for attendance on Wednesday evening is 470. Which of the following is the appropriate conclusion at the 5% level of significance? A) We cannot conclude that the mean attendance differs because the p-value 0.0019 < 0.05. B) We cannot conclude that the mean attendance differs because the p-value 0.0037 < 0.05. C) We can conclude that the mean attendance differs because the p-value 0.0037 < 0.05. D) We can conclude that the mean attendance differs because the p-value 0.0019 < 0.05.

C) We can conclude that the mean attendance differs because the p-value 0.0037 < 0.05.

We draw a random sample of size 25 from a normal population with variance 2.4. If the sample mean is 12.5, what is a 99% confidence interval for the population mean? A) [11.7793, 13.2207] B) [11.3835, 13.6165] C) [11.7019, 13.2981] D) [11.2600, 13.7400]

C) [11.7019, 13.2981]

We draw a random sample of size 25 from a normal population with variance 2.2. If the sample mean is 18.5, what is a 90% confidence interval for the population mean? A) [17.6935, 19.3065] B) [18.0893, 18.9107] C) [18.0120, 18.9880] D) [17.5700, 19.4300]

C) [18.0120, 18.9880]

A statistics student is asked to estimate y = β0 + β1x + ε. She calculates the following values: ∑xi = 248, ∑(xi − x )2 = 429, ∑(xi − x ) (yi − y ) = −568, ∑yi = 413, ∑(yi − y )2 = 1108, n = 11. Which of the following is the sample regression equation? A) y ^ = 67.31 + 1.32x B) y ^ = 15.71 − 1.32x C) y ^ = 67.31 − 1.32x D) y ^ = 15.71 + 1.32x

C) y ^ = 67.31 − 1.32x

The owner of a large car dealership believes that the financial crisis decreased the number of customers visiting her dealership. The dealership has historically had 800 customers per day. The owner takes a sample of 100 days and finds the average number of customers visiting the dealership per day was 750. Assume that the population standard deviation is 310. The value of the test statistic is ________. A) t99 = 1.6130 B) t99 = −1.6130 C) z = −1.6130 D) z = 1.6130

C) z = −1.6130

A city in California spent $5 million repairing damage to its public buildings in 2017. The following table shows the categories where the money was directed. Cause Percent Termites 35 % Water Damage 6 % Mold 11 % Earthquake 29 % Other 19 % How much did the city spend to fix damage caused by mold? A) $1,500,000 B) $550,000 C) $1,100,000 D) $275,000

D) $275,000

Let P(A) = 0.70, P(B|A) = 0.70, and P(B|Ac) = 0.27. Compute P(B). A) 0.345 B) 0.42 C) 0.37 D) 0.57

D) 0.57

The number of cars sold by a car salesperson during each of the last 25 weeks is the following: Number Sold Frequency 0 10 1 10 2 5 What is the probability that the salesperson sells no more than one car during a week? A) 0.20 B) 0.60 C) 0.40 D) 0.80

D) 0.80

The following table shows the number of cars sold last month by six dealers at Centreville Nissan dealership and their number of years of sales experience. Years of Experience Sales 4 12 2 8 6 8 6 12 8 18 1 7 Management would like to use simple regression analysis to estimate monthly car sales using the number of years of sales experience. The slope of the regression equation is equal to ________. A) −-3.53 B) 6.35 C) 0.91 D) 1.20

D) 1.20

The GPA of accounting students in a university is known to be normally distributed. A random sample of 32 accounting students results in a mean of 2.64 and a standard deviation of 0.15. Construct the 95% confidence interval for the mean GPA of all accounting students at this university. A) 2.64 ± 1.96 (0.15 / 32) B) 2.64 ± 2.086 (0.15 / 32) C) 2.64 ± 1.729 (0.15 / 32) D) 2.64 ± 2.040 (0.15 / 32)

D) 2.64 ± 2.040 (0.15 / 32)

San Francisco 49ers' linebacker Patrick Willis won the Defensive Rookie of the Year Award in 2007 with a total of 232 tackles. Tackles are measured on what kind of a scale? Is a variable measuring the number of tackles considered continuous or discrete? A) Interval scale; discrete B) Interval scale; continuous C) Ratio scale; continuous D) Ratio scale; discrete

D) Ratio Scale; Discrete

Recently, six single-family homes in Corpus Christi in Texas sold at the following prices (in $1,000s): 574, 474, 697, 539, 621, 610. Find a 95% confidence interval for the mean sale price in Corpus Christi. A) [528.96, 642.64] B) [496.80, 674.80] C) [510.40, 661.20] D) [505.85, 665.75]

D) [505.85, 665.75]

An advertisement for a popular weight-loss clinic suggests that participants in its new diet program lose, on average, more than 10 pounds. A consumer activist decides to test the authenticity of the claim. She follows the progress of 29 women who recently joined the weight-reduction program. She calculates the mean weight loss of these participants as 10.8 pounds with a standard deviation of 1.6 pounds. The test statistic for this hypothesis would be ________. A) z = 2.693 B) z = −2.693 C) t28 = −2.693 D) t28 = 2.693

D) t28 = 2.693

Mutually exclusive and collectively exhaustive events contain all outcomes of a sample space, and they do not share any common outcomes. TRUE OR FALSE

TRUE

The required sample size for the interval estimation of the population mean µ can be computed if we specify the population standard deviation σ, the value of Zα/2 based on the confidence level 100(1 − α)% and the desired margin of error E. TRUE OR FALSE

TRUE