BSTAT 2305 FINAL

An investor bought common stock of Blackstone Company on several occasions at the following prices.The following frequency distribution represents the number of shares and its price per share. Number of Shares - Price per Share 100 - $40 200 - $32 400 - $26 The average price per share at which the investor bought these shares of common stock was the closest to __________.

$29.71 x = (100 × 34 + 200 × 30 + 400 × 28)/(100 + 200 + 400) = 100/700 × 34 + 200/700 × 30 + 400/700 × 28 = 29.43.

The starting salary of an administrative assistant is normally distributed with a mean of $50,000 and a standard deviation of $2,500. We know that the probability of a randomly selected administrative assistant making a salary between μ − x and μ + x is 0.7416. Find the salary range referred to in this statement.

$47,175 to $52,825 The appropriate Excel function is =NORM.INV(((1−0.7416)/2),50000,2500) = $47,175 ANDExcel function is =NORM.INV((0.7416+(1−0.7416)/2),50000,2500) = $52,825

Professors at a local university earn an average salary of $80,000 with a standard deviation of $6,000. With the beginning of the next academic year, all professors will get a 2% raise. What will be the average and the standard deviation of their new salaries?

$81,600 and $6,120. The sample mean and sample standard deviation should be multiplied by 1.02.

Consider the following probability distribution. xi - P(X = x i) -2 - 0.2 -1 - 0.1 0 - 0.3 1 - 0.4 The expected value is _____.

-0.1 E(X) = −2 × 0.20 + −1 × 0.10 + 0 × 0.30 + 1 × 0.40 = −0.1

The annual returns (in percent) for a sample of stocks in the technology industry over the past year are as follows: 4.2 −9.4 2.8 −16.0 −6.6 The average return is the closest to __________.

-5 In Excel, the function used is =AVERAGE(4.2,−9.4,2.8,−16.0,−6.6) = −5

The annual returns (in percent) for a sample of stocks in the technology industry over the past year are as follows: 4.2 −9.4 2.8 −16.0 −6.6 The median return is the closest to __________.

-6.6 In Excel, the function used is =MEDIAN(4.2,-9.4,2.8,−16.0,−6.6) = −6.6

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 12 minutes. A random sample of 45 employees were selected and they averaged 12.6 minutes. It is believed that the population standard deviation is 2.2 minutes. The α is set to 0.05. The p-value for this hypothesis test would be __________.

0.0337 The appropriate Excel function isp-value =1-NORM.S.DIST((12.6-12)/(2.2/SQRT(45)),TRUE) = 0.0337

Suppose the life of a particular brand of laptop battery is normally distributed with a mean of 8 hours and a standard deviation of 0.6 hours. What is the probability that the battery will last more than 9 hours before running out of power?

0.0478 Compute P(X > 9). Note that P(Z > z) = 1 - P(Z < z). The appropriate Excel function is =1-NORM.DIST(9,8,0.6,TRUE) = 0.0478

Gold miners in Alaska have found, on average, 12 ounces of gold per 1,000 tons of dirt excavated with a standard deviation of 3 ounces. Assume the amount of gold found per 1,000 tons of dirt is normally distributed. What is the probability the miners find more than 16 ounces of gold in the next 1,000 tons of dirt excavated?

0.0912 The appropriate Excel function is =1-NORM.DIST(16,12,3,TRUE) =0.0912

The probability P(Z > 1.28) is closest to ______.

0.10 Compute P(Z > z) = 1− P(Z ≤ z).

Calculate the value of R2 given the ANOVA portion of the following regression output:

0.151 R^2 = 1 - (SSE/SST) = (SSR/SST) , where SSR is the regression sum of squares. (SS Regression/ SS Total)

A superstar major league baseball player just signed a new deal that pays him a record amount of money. The star has driven in an average of 110 runs over the course of his career, with a standard deviation of 31 runs. An average player at his position drives in 80 runs. What is the probability the superstar bats in fewer runs than an average player next year? Assume the number of runs batted in is normally distributed.

0.1666 The appropriate Excel function is =NORM.DIST(80,110,31,TRUE) = 0.1666

Consider the following cumulative distribution function for the discrete random variable X. x - P(X ≤ x) 1 - 0.32 2 - 0.49 3 - 0.84 4 - 1.00 What is the probability that X equals 2?

0.17 P(X = 2) = P(X ≤ 2) - P(X ≤ 1) = 0.49 − 0.32 = 0.17

Suppose the round-trip airfare between Boston and Orlando follows the normal probability distribution with a mean of $387.20 and a standard deviation of $68.50. What is the probability that a randomly selected airfare between Boston and San Francisco will be more than $450?

0.1796 Compute P(X > $450). Use z table that provides cumulative probabilities P(Z ≤ z) for positive and negative values of z. Compute P(Z > z) = 1 − P(Z ≤ z). The appropriate Excel function is =1-NORM.DIST(450,387.2,68.5,TRUE) = 0.1796

Mark Zuckerberg, the founder of Facebook, announced that he will eat meat only from animals that he has killed himself (Vanity Fair, November 2011). Suppose 257 people were asked, "Does the idea of killing your own food appeal to you, or not?" The accompanying contingency table, cross-classified by gender, is produced from the 187 respondents. Male - Female Yes - 35 - 20 No - 56 - 76 The probability that a respondent is male and feels that the idea of killing his own food is appealing is the closest to _____.

0.19 P(Male∩Yes) = 35/187 = 0.19

Consider the following cumulative distribution function for the discrete random variable X. x - P(X ≤ x) 1 - 0.10 2 - 0.35 3 - 0.75 4 - 0.85 5 - 1.00 What is the probability that X is greater than 3?

0.25 P(X ≤ 3) = 1 −P(X ≤ 3) = 1 − 0.75 = 0.25

The following probability table shows probabilities concerning Favorite Subject and Gender. What is the probability of selecting an individual preferring science if she is female?

0.2609 P(Science∣∣Female)=0.150/0.575=0.2609

For any normally distributed random variable with mean μ and standard deviation σ, the proportion of the observations that fall outside the interval [μ − σ, μ + σ] is the closest to ______.

0.3174 The empirical rule states that P(μ − σ ≤ X ≤ μ + σ) = 0.6826. Thus, 1 − 0.6826 = 0.3174

Suppose the average price of gasoline for a city in the United States follows a continuous uniform distribution with a lower bound of $3.50 per gallon and an upper bound of $3.80 per gallon. What is the probability a randomly chosen gas station charges more than $3.70 per gallon?

0.3333 =(3.8 − 3.7)/(3.8 − 3.5) =0.3333

Let P(A) = 0.3 and P(B) = 0.4. Suppose A and B are independent. What is the value of P(B|A)?

0.4

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 will sell one car during a week?

0.40 P(X = 1) = 10/25 = 0.40

Consider the following cumulative distribution function for the discrete random variable X. x - P(X ≤ x) 1- 0.30 2- 0.44 3 - 0.72 4 - 1.00 What is the probability that X is less than or equal to 2?

0.44

Consider the following discrete probability distribution. x - P(X = x) -10 - 0.35 0 - 0.10 10 - 0.15 20 - 0.40 What is the probability that X is less than 5?

0.45 P(X < 5) = P(X = −10) + P(X = 0) = 0.35 + 0.10 = 0.45

A company is bidding on two projects, A and B. The probability that the company wins project A is 0.40 and the probability that the company wins project B is 0.25. Winning project A and winning project B are independent events. What is the probability that the company does not win either project?

0.45 The addition rule is calculated as P(A∪B) = P(A) + P(B − P(A∩B). A complement rule is P(A) = 1 − P(A^c). P(A∪B) = 0.40 + 0.25 − 0.1 = 0.55 Neither = 1 − P(A∪B) = 1 − 0.55 = 0.45

A multiple regression model with two explanatory variables is estimated using 20 observations resulting in SSE = 550 and SST = 1000. Which of the following is the correct value of R2?

0.45 The coefficient of determination is computed as R^2 = 1 − SSE/SST.

Find the probability P(−1.96 ≤ Z ≤ 0).

0.4750 Compute P(z1 ≤ Z ≤ z2) = P(Z ≤ z2) − P(Z ≤ z1).

Mark Zuckerberg, the founder of Facebook, announced that he will eat meat only from animals that he has killed himself (Vanity Fair, November 2011). Suppose 257 people were asked, "Does the idea of killing your own food appeal to you, or not?" The accompanying contingency table, cross-classified by gender, is produced from the 187 respondents. Male - Female Yes - 35 - 20 No - 56 - 76 The probability that a respondent to the survey is male is the closest to ____.

0.49 P(Male)=(35+56)/187=0.49

The probability that a normal random variable is less than its mean is ______.

0.5

Two hundred people were asked if they had read a book in the last month. The accompanying contingency table, cross-classified by age, is produced. Under 30 - 30+ Yes - 76 - 65 No - 24 - 35 The probability that a respondent is at least 30 years old is the closest to ______.

0.50 P(30+) = 100/200 = 0.50

A company is bidding on two projects, A and B. The probability that the company wins project A is 0.40 and the probability that the company wins project B is 0.25. Winning project A and winning project B are independent events. What is the probability that the company wins project A or project B?

0.55 The addition rule is calculated as P(A∪B) = P(A) + P(B) − P(A∩B). Since the events are independent, then the P(A&B) = P(A) × P(B) = 0.4 × 0.25 = 0.1 Hence P(A or B) = 0.4 + 0.25 − 0.1 = 0.55

According to a study by the Centers for Disease Control and Prevention, about 33% of U.S. births are Caesarean deliveries. Suppose seven expectant mothers are randomly selected. What is the probability that at most two of the expectant mothers will have a Caesarean delivery?

0.5783 The Excel function used is = BINOM.DIST(2,7,0.33,TRUE) = 0.5783

A bank manager estimates that an average of two customers enters the tellers' queue every five minutes. Assume that the number of customers that enters the tellers' queue is Poisson distributed. What is the probability that at least two customers enter the queue in a randomly selected five-minute period?

0.5940 The Excel function used is =1−POISSON.DIST(1,2,TRUE) = 0.5940

Consider the following discrete probability distribution. x - P(X = x) -10 - 0.29 0 - 0.09 10 - 0.13 20 - 0.49 What is the probability that X is greater than 0?

0.62 P(X > 0) = P(X = 10) + P(X = 20) = 0.13 + 0.49 = 0.62

A survey of adults who typically work full time from home recorded their current education level. The results are shown in the table below. The probability that a randomly selected adult who works full time from home has a bachelor's degree or higher is ______.

0.64 We use the relative frequency to calculate the empirical probability of event A as P(A)= the number of outcomes in A / the number of outcomes in S p(Bachelors) = 32/(32+12+4+2) = 0.64

Thirty percent of the CFA candidates have a degree in economics. A random sample of three CFA candidates is selected. What is the probability that at least one of them has a degree in economics?

0.657 The Excel function used is =1-BINOM.DIST(0,3,0.3,TRUE) = 0.657

An analyst has a limit order outstanding on a stock. He argues that the probability that the order will execute before the close of trading is 0.30. What is the probability that the order will execute after the closing of trading?

0.70 The probability that the order will execute after the closing of trading = 1 − 0.3 = 0.7.

The number of homes sold by a realtor during a month has the following probability distribution: Number Sold - Probability 0 - 0.20 1 - 0.40 2 - 0.40 What is the standard deviation of the number of homes sold by the realtor during a month?

0.75 The standard deviation of the discrete random variable X is calculated as SD(X)=σ=√σ^2. The variance of the discrete random variable X is calculated as Var(X) = σ^2 = ∑(xi − μ)^2 P(X = xi). E(X) = 0 × 0.20 + 1 × 0.40 + 2 × 0.40 = 1.2 Var(X) = (0 − 1.2)^2 × 0.20 + (1 − 1.2)^2 × 0.40 + (2 − 1.2)2 × 0.40 = 0.56 SD(X) = √0.56 = 0.75

As of September 30, the earnings per share (EPS) of five firms in the beverages industry are as follows: 1.13 2.41 1.52 1.40 0.41 The 25th percentile and the 75th percentile of the EPS are the closest to __________.

0.77 and 1.97 In Excel, the functions used are =QUARTILE.EXC(<data>,1) = 0.77 and =QUARTILE.EXC(<data>,3) = 1.97.

The time for a professor to grade a student's homework in statistics is normally distributed with a mean of 12.4 minutes and a standard deviation of 2.4 minutes. What is the probability that randomly selected homework will require less than 16 minutes to grade?

0.9332 Compute P(X < 16). Use z table that provides cumulative probabilities P(Z ≤ z) for positive and negative values of z. the appropriate Excel function is =NORM.DIST(16,12.4,2.4,TRUE) = 0.9332.

Consider the following probability distribution. xi - P(X = xi) 0 - 0.1 1 - 0.2 2 - 0.4 3 - 0.3 The standard deviation is _________.

0.94 The variance of the discrete random variable X is calculated as Var(X) = σ^2 = Σ(xi − μ)^2 P(X = xi). E(X) = 0 × 0.10 + 1 × 0.20 + 2 × 0.40 + 3 × 0.30 = 1.9 Var(X) = (0 − 1.9)2 × 0.10 + (1 − 1.9)2 × 0.20 + (2 − 1.9)2 × 0.40 + (3 − 1.9)2 × 0.30 = 0.89 SD(X)=√0.89=0.94

For a particular clothing store, a marketing firm finds that 16% of $10-off coupons delivered by mail are redeemed. Suppose six customers are randomly selected and are mailed $10-off coupons. What is the expected number of coupons that will be redeemed?

0.96 The expected value of a binomial random variable is calculated as E(X) = μ = np. μ = 6 × 0.16 = 0.96

A statistics professor works tirelessly to catch students cheating on his exams. He has particular routes for his teaching assistants to patrol, an elevated chair to ensure an unobstructed view of all students, and even a video recording of the exam in case additional evidence needs to be collected. He estimates that he catches 95% of students who cheat in his class, but 1% of the time that he accuses a student of cheating he is actually incorrect. Consider the null hypothesis, "the student is not cheating." What is the probability of a Type I error?

1%

The manager at a water park constructed the following frequency distribution to summarize attendance in July and August. What of the following is the most likely attendance range?

1,000 up t0 1,750 For quantitative data, a relative frequency distribution identifies the proportion of observations that falls into each class: class relative frequency is equal to the class frequency divided by total number of observations. In this case, the 1,000 up to 1,750 class is made up of three classes (5+6+10 = 21), which is greater than any other answer choice class.

Consider the following probability distribution. xi - P(X = xi) 0 - 0.5 1 - 0.1 2 - 0.2 3 - 0.2 The expected value is _____.

1.1 E(X) = 0 × 0.5 + 1 × 0.1 + 2 × 0.2 + 3 × 0.2 = 1.1

According to geologists, the San Francisco Bay Area experiences five earthquakes with a magnitude of 6.5 or greater every 100 years. What is the standard deviation of the number of earthquakes with a magnitude of 6.5 or greater striking the San Francisco Bay Area in the next 40 years?

1.414 5 earthquakes/100 years relates to 2 earthquakes/40 years σ = √2 = 1.414

As of September 30, the earnings per share (EPS) of five firms in the biotechnology industry are 1.59 2.42 2.13 1.80 0.05 The sample mean and the sample standard deviation are the closest to __________.

1.6 and 0.92 In Excel, the function used is =AVERAGE(1.59,2.42,2.13,1.80,0.05) = 1.60 and =STDEV.S(1.59,2.42,2.13,1.80,0.05) = 0.92.

An advertisement for a popular weight-loss clinic suggests that participants in its new diet program lose, on average, more than 11 pounds. A consumer activist decides to test the authenticity of the claim. She follows the progress of 28 women who recently joined the weight-reduction program. She calculates the mean weight loss of these participants as 11.8 pounds with a standard deviation of 2.3 pounds. The test statistic for this hypothesis would be __________.

1.84 t-score = (11.8−11)/(2.3/√28) = 1.8405

Consider the following probability distribution. xi - P(X = xi) 0 - 0.1 1 - 0.2 2 - 0.4 3 - 0.3 The expected value is _____.

1.90 The variance of the discrete random variable X is calculated as Var(X) = σ^2 = ∑(xi - μ)^2 P(X = xi). E(X) = 0 × 0.10 + 1 × 0.20 + 2 × 0.40 + 3 × 0.30 = 1.9 Var(X) = (0 - 1.9)^2 × 0.10 + (1 - 1.9)^2 × 0.20 + (2 - 1.9)^2 × 0.40 + (3 - 1.9)^2 × 0.30 = 0.89

The accompanying relative frequency distribution represents the last year car sales for the sales force at Kelly's Mega Used Car Center. If Kelly's employs 100 salespeople, how many of these salespeople have sold at least 45 but fewer than 65 cars in the last year?

46 (0.15 + 0.31)100 = 46 employees.

According to a report in USA Today, more and more parents are helping their young adult children get homes. Suppose eight persons in a random sample of 40 young adults who recently purchased a home in Kentucky received help from their parents. You have been asked to construct a 95% confidence interval for the population proportion of all young adults in Kentucky who received help from their parents. What is the margin of error for a 95% confidence interval for the population proportion?

1.96(0.0632) The appropriate Excel functions arez-score =NORM.S.INV(1-0.05/2) = 1.96 standard error =SQRT(8/40*(1-8/40)/40) = 0.0632

The ages of MBA students at a university are normally distributed with a known population variance of 10.24. Suppose you are asked to construct a 95% confidence interval for the population mean age if the mean of a sample of 36 students is 26.5 years. What is the margin of error for a 95% confidence interval for the population mean?

1.96(3.20/6) The margin of error is computed as zα/2(σ/√n). Use z table.

The following histogram represents the number of pages in each book within a collection. What is the frequency of books containing at least 250 but fewer than 400 pages?

11 Add the frequencies, 7, 3, and 1, for the classes 250 up to 300, 300 up to 350, and 350 up to 400.

Sales for Adidas grew at a rate of 0.5196 in Year 1, 0.0213 in Year 2, 0.0485 in Year 3, and −0.0387 in Year 4. The average growth rate for Adidas during these four years is the closest to __________.

11.83%

The waiting time at an elevator is uniformly distributed between 30 and 200 seconds. Find the mean and standard deviation of the waiting time.

115 seconds and 49.07 seconds μ = (30 + 200)/2 and σ = SQRT((200 − 30)^2/12) =115 seconds and 49.07 seconds

The following data represent scores on a pop quiz in a statistics section. 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 __________.

14 Class width = (Maximum − Minimum)/(Number of classes) = (89 −21)/5 = 13.60 ≈ 14 (We always round up.)

There are 30 Major League Baseball teams in the National League. Five of these teams will make the playoffs at the end of the season. The number of unique groups of teams that can make the playoffs is ______.

142,506 In Excel, the function used is =COMBIN(30,5) = 142,506

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. What percentage of houses has an asking price between $350,000 and under $400,000?

18.9% In this case, (10 + 13 + 4 + 12) / (10 + 13 + 4 + 12 + 14) = (expression error)/(expression error) = 18.90%.

Consider the following data: 1, 2, 4, 5, 10, 12, 18. The 30th percentile is the closest to __________.

2.8 In Excel, the function used is =PERCENTILE.EXC(<data>,0.30) = 2.8.

There are 23 chess players participating in a weekend tournament. Prices are awarded to the first-, second-, third-, and fourth-place finishers. The number of different ways these four places can be filled by those playing is ______.

212,520 In Excel, the function used is =PERMUT(23,4) = 212,520

The following data represent the recent sales price (in $1,000s) of 24 homes in a Midwestern city. Suppose the data on house prices will be grouped into five classes. The width of the classes for a frequency distribution or histogram is the closest to __________.

26 Width of class = (maximum value − minimum value)/(Number of classes) Width = (244 − 114)/5 = 26.00; so round up to 26.

Let X be normally distributed with mean µ = 25 and standard deviation σ = 5. Find the value x such that P(X ≥ x) = 0.1736.

29.70 The appropriate Excel function is =NORM.INV(1-0.1736,25,5) =29.70

An experiment consists of tossing three fair coins. What is the probability of tossing two tails?

3/8

The accompanying relative frequency distribution represents the last year car sales for the sales force at Kelly's Mega Used Car Center. 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?

4 0.04(100) = 4 employees

A marketing analyst wants to examine the relationship between sales (in $1,000s) and advertising (in $100s) for firms in the food and beverage industry and collects monthly data for 25 firms. He estimates the model: Sales = β0 + β1 Advertising + ε. The following ANOVA table shows a portion of the regression results. Which of the following is the standard error of the estimate?

4.68 The standard error of the estimate se is a point estimate of the standard deviation of the random error ε, and is computed as se = √MSE , where MSE is the mean square error for the residuals. √MS Residual

An investment consultant tells her client that the probability of making a positive return with her suggested portfolio is 0.90. What is the risk, measured by standard deviation that this investment manager has assumed in her calculation if it is known that returns from her suggested portfolio are normally distributed with a mean of 6%?

4.69% First, find z by: The appropriate Excel function is =NORM.S.INV(1−0.9) = −1.28. Then, σ = (0 − 6)/−1.28 = 4.69

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 65 cars in the last year?

47 (0.22 + 0.25)100 = 47 employees.

5! is equal to _______.

5 × 4 × 3 × 2 × 1

The following frequency distribution displays the weekly sales of a certain brand of television at an electronics store. How many weeks of data are included in this frequency distribution?

50 If we sum the frequency column, we obtain the sample size.

The accompanying table shows students' scores from the final exam in a history course. Scores - Cumulative Frequency 50 up to 60 - 16 60 up to 70 - 38 70 up to 80 - 63 80 up to 90 - 92 90 up to 100 - 100 How many of the students scored at least 70 but less than 90?

54 Ninety-Two students scored less than 90, and 38 students scored less than 70. The total that scored at least 70 but less than 90 equals the number that scored less than 90 minus the number that scored less than 70: 92 − 38 = 54.

Total revenue for Apple Computers (in millions) was $42,905 in Year 1, $65,225 in Year 2, and $108,249 in Year 3. The average growth rate of revenue during these three years is the closest to __________.

58.84% =(108,249/42,905)^(1/2) − 1 = 58.84%

The following stem-and-leaf diagram shows the speeds in miles per hour (mph) of 14 cars approaching a toll booth on a bridge in Oakland, California. How many of the cars were traveling faster than 25 mph but slower than 40 mph?

6 26, 31, 31, 33, 37, and 38.

Suppose the wait to pass through immigration at JFK Airport in New York is thought to be bell-shaped and symmetrical with a mean of 22 minutes. It is known that 68% of travelers will spend between 16 and 28 minutes waiting to pass through immigration. The standard deviation for the wait time through immigration is __________.

6 minutes Since 68% is one standard deviation from the mean, then 28 − 22 = 6 or 22 − 16 = 6 minutes

The time of a call to a technical support line is uniformly distributed between 2 and 10 minutes. What are the mean and variance of this distribution?

6 minutes and 5.3333 (minutes)^2 μ = (10 + 2)/2 and σ = (10 − 2)^2/12 = 6 minutes and 5.3333 (minutes)^2

Consider a population with data values of 12 8 28 22 12 30 14 The population variance is the closest to __________.

64.00 In Excel, the function used is =VAR.P(12,8,28,22,12,30,14) = 64; Wrong answer would be using the sample variance of =VAR.S().

An investor has a $200,000 portfolio of which $120,000 has been invested in Stock A and the remainder in Stock B. Other characteristics of the portfolio are shown in the accompanying table. The portfolio variance is ______.

66.78 (%)^2 ωA = 120,000/200,000 = 0.60; ωB = 80,000/200,000 = 0.40 Var(RP ) = 11.82^2 × 0.60^2 + 7.19^2 × 0.40^2 + 2 × 0.60 × 0.40 × 17.10 = 66.78

An investor has a $100,000 portfolio of which $75,000 has been invested in Stock A and the remainder in Stock B. Other characteristics of the portfolio are shown in the accompanying table. The expected return of the portfolio is _____.

7.38% E(RP ) = 8.0 × 75,000/100,000 + 5.5 × 25,000/100,000 = 7.38

Consider a population with data values of 12 8 28 22 12 30 14 The population standard deviation is the closest to __________.

8.00 In Excel, the function used is =STDEV.P(12,8,28,22,12,30,14) = 8; Wrong answer would be using the sample standard deviation of =STDEV.S()

Romi, a production manager, is trying to improve the efficiency of his assembly line. He knows that the machine is set up correctly only 70% of the time. He also knows that if the machine is set up correctly, it will produce good parts 95% of the time, but if set up incorrectly, it will produce good parts only 40% of the time. Romi 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?

84.7% (0.95×0.70)/(0.95×0.70+0.40×(1−0.70)) = 0.847

An investor has a $100,000 portfolio of which $75,000 has been invested in Stock A and the remainder in Stock B. Other characteristics of the portfolio are shown in the accompanying table. The standard deviation of the portfolio is _____.

9.39 (%) The portfolio variance is calculated as Var(Rp)=w^2Aσ^2A + w^2Bσ^2B + 2wAwBρABσAσB. ωA=75,000/100,000=0.75; ωB=250,000/100,000=0.25 Var(RP) = 11.822 × 0.752 + 7.192 × 0.252 + 2 × 0.75 × 0.25 × 17.10 = 88.23SD(RP)=√88.23=9.39

Given an experiment in which a fair coin is tossed three times, the sample space is S = {HHH, HHT, HTH, THH, HTT, THT, TTH, TTT}. Event A is defined as tossing one head (H). What is the event A^c and what is the probability of this event?

A^c = {TTT, HHT, HTH, THH, HHH}; P(A^c) = 0.625 The complement of event A, Ac, is the event consisting of all outcomes in the sample space S that are not in A. Of the 8 outcomes, we only want those that have two heads or no heads. This makes 5 outcomes and 5/8 = 0.625.

The minimum sample size n required to estimate a population mean with 95% confidence and the assumed estimate of the population standard deviation 6.5 was found to be 124. Which of the following is the approximate value of the assumed desired margin of error?

D = 1.1441 The appropriate Excel function is margin of error =SQRT((NORM.S.INV(1-0.05/2)*6.5)^2/124) = 1.1441

Assume the sample space S = {win, loss}. Select the choice that fulfills the requirements of the definition of probability.

P({win}) = 0.7, P({loss}) = 0.3

If X has a normal distribution with µ = 100 and σ = 5, then the probability P(90 ≤ X ≤ 95) can be expressed in terms of a standard normal variable Z as ______.

P(−2 ≤ Z ≤ −1) z = (90 − 100)/5 = −2 and z = (95 − 100)/5 = −1

The director of graduate admissions 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.

The correlation between GRE and GPA is positive and strong. =CORREL(<GRE data>,<GPA data>) = 0.894

The birth weight for babies is normally distributed with a mean of 7.5 lb and a standard deviation of 1.125 lb. Suppose a pediatrician claims that the average birth weight for babies under her care is greater than 7.5 lb. She randomly selects 30 newborns and produces an average birth weight of 8 lb. Which of the following is true if the pediatrician uses a p-value approach to implement a hypothesis test at a 5% significance level to support her claim?

The p-value = p( X ≥ 7.5) = P(Z ≥ 2.434) = 0.0075 (8 − 7.5)/(1.125/sqrt(30)) = 2.434. The p-value = 1-NORM.S.DIST(2.434,TRUE) = 0.0075.

A professional sports organization is going to implement a test for steroids. The test gives a positive reaction in 94% of the people who have taken the steroid. However, it erroneously gives a positive reaction in 4% of the people who have not taken the steroid. What is the probability of Type I and Type II errors giving the null hypothesis "the individual has not taken steroids."

Type I: 4%, Type II: 6%

The Department of Education would like to test the hypothesis that the average debt load of graduating students with a bachelor's degree is equal to $17,000. A random sample of 29 students had an average debt load of $18,200. It is believed that the population standard deviation for student debt load is $3,900. The α is set to 0.05. The confidence interval for this hypothesis test would be __________.

[$16,780.54, $19,619.46] The confidence interval for the two-tailed hypothesis test is computed as [x - zα/2 σ/√n,x + zα/2 σ/√n]. Lower limit = (18,200 − 1.96 × 3,900)/√29 = $16,780.54 Upper limit = (18,200 + 1.96 × 3,900)/√29 = $19,619.46

In an examination of purchasing patterns of shoppers, a sample of 16 shoppers revealed that they spent, on average, $54 per hour of shopping. Based on previous years, the population standard deviation is thought to be $21 per hour of shopping. Assuming that the amount spent per hour of shopping is normally distributed, find a 90% confidence interval for the mean amount.

[$45.36, $62.64] The appropriate Excel functions are Lower Limit =54-CONFIDENCE.NORM(0.1,21,16) = 45.36 Upper Limit =54+CONFIDENCE.NORM(0.1,21,16) = 62.64

A sample of 2,005 American adults was asked how they viewed China, with 15% of respondents calling the country "unfriendly" and 7% of respondents indicating the country was "an enemy." Construct a 95% confidence interval of the proportion of American adults who viewed China as either "unfriendly" or "an enemy."

[0.2019, 0.2381] The appropriate Excel functions are Lower Limit =0.22-NORM.S.INV(1-0.05/2)*SQRT(0.22*(1-0.22)/2,005) = 0.2019 Upper Limit =0.22+NORM.S.INV(1-0.05/2)*SQRT(0.22*(1-0.22)/2,005) = 0.2381

A machine that is programmed to package 1.90 pounds of cereal is being tested for its accuracy in a sample of 45 cereal boxes, the sample mean filling weight is calculated as 1.92 pounds. The population standard deviation is known to be 0.06 pounds. Find the 95% confidence interval for the mean.

[1.90, 1.94] The appropriate Excel functions areLower Limit =1.92-CONFIDENCE.NORM(0.05,0.06,45) = 1.90Upper Limit =1.92+CONFIDENCE.NORM(0.05,0.06,45) = 1.94

We draw a random sample of size 49 from the normal population with variance 2.0. If the sample mean is 12.5, what is a 95% confidence interval for the population mean?

[12.1040, 12.8960] The appropriate Excel functions areLower Limit =12.5-CONFIDENCE.NORM(0.05,SQRT(2.0),49) = 12.1040.Upper Limit =12.5+CONFIDENCE.NORM(0.05,SQRT(2.0),49) = 12.8960.

Given a sample mean of 27 and a sample standard deviation of 3.5 computed from a sample of size 36, find a 95% confidence interval on the population mean.

[25.8158, 28.1842] The appropriate Excel functions are Lower Limit =27-CONFIDENCE.T(0.05,3.5,36) = 25.8158 Upper Limit =27+CONFIDENCE.T(0.05,3.5,36) = 28.1842

A website advertises job openings on its website, but job seekers have to pay to access the list of job openings. The website recently completed a survey to estimate the number of days it takes to find a new job using its service. It took the last 39 customers an average of 60 days to find a job. Assume the population standard deviation is 10 days. Calculate a 90% confidence interval of the population mean number of days it takes to find a job.

[57.3661, 62.6339] Because the population standard deviation is known the confidence interval of the population mean is computed as x +- zα/2 σ/√n. Use z table. The appropriate Excel functions are Lower Limit =60-CONFIDENCE.NORM (0.10,10,39) = 57.3661 Upper Limit =60+CONFIDENCE.NORM (0.10,10,39) = 62.6339

What is the minimum sample size required to estimate a population mean with 90% confidence when the desired margin of error is D = 1.25? The standard deviation in a preselected sample is 8.5.

n = 126 For a desired margin of error E, the minimum sample size n required to estimate a 100(1−α)% confidence interval for the population mean is computed as n = ((zα⁢/2⁢⁢ σ)/E)^2. σ⁢ ^ is a reasonable estimate of σσ⁢ in the planning stage. Use z table. The appropriate Excel function is Sample size =(NORM.S.INV(1-0.1/2)*8.5/1.25)^2 = 125.1043, rounds up to 126.

A university is interested in promoting graduates of its honors program by establishing that the mean GPA of these graduates exceeds 3.50. A sample of 36 honors students is taken and is found to have a mean GPA equal to 3.60. The population standard deviation is assumed to equal 0.40. The value of the test statistic is __________.

z = 1.50 z-score = (3.6 − 3.5)/(0.4/√36) =1.5000

Find the z value such that P(−z ≤ Z ≤ z) = 0.95.

z = 1.96

For an experiment in which a single die is rolled, the sample space is __________.

{2, 1, 3, 6, 5, 4}.

In an experiment in which a coin is tossed twice, which of the following represents mutually exclusive and collectively exhaustive events?

{TT, HH} and {TH, HT}

Which of the following are mutually exclusive events of an experiment in which two coins are tossed?

{TT, HH} and {TH}

Which of the following is true regarding the weighted mean formula: =Σwixi for i = 1, ..., n

Σwi = 1 =CORREL(<GRE data>,<GPA data>) = 0.894