ISDS 2000 Final pt. 1
According to the recent report, scientists in New England say they have identified a set of genetic variants that predicts extreme longevity with 77% accuracy. Assume 150 patients decide to get their genome sequenced. If the claim by scientists is accurate, what is the probability that more than 120 patients will get a correct diagnosis for extreme longevity?
0.1913 The appropriate Excel function is =1-NORM.DIST(120/150,0.77,SQRT(0.77*(1-0.77)/150),TRUE) = 0.1913
Let P(A∩B)=.3, and P(A∩Bc)=0.15 , and P(Ac∩B)=0.35. Compute P(Ac∩Bc)
0.20 =1−P(A∪B) =1−(P(A∩B))+(P(A∩Bc))+(P(Ac∩B)) = 1 − (0.3 + 0.15 + 0.35) = 0.20
The average time between trades for a high-frequency trading investment firm is 40 seconds. Assume the time between trades is exponentially distributed. What is the probability that the time between trades for a randomly selected trade and the one proceeding it is more than a minute?
0.2231 The appropriate Excel function is =1-EXPON.DIST(60,1/40,TRUE) = 0.2231
Suppose that, on average, electricians earn approximately µ = $54,000 per year in the United States. Assume that the distribution for electricians' yearly earnings is normally distributed and that the standard deviation is σ = $12,000. What is the probability that the average salary of four randomly selected electricians is less than $50,000?
0.2525 The appropriate Excel function is =NORM.DIST(50000,54000,12000/SQRT(4),TRUE) = 0.2525
Suppose 35% of homes in a Miami, Florida, neighborhood are under water (in other words, the amount due on the mortgage is larger than the value of the home). There are 160 homes in the neighborhood and 30 of those homes are owned by your friends. What is the probability that fewer than 30% of your friends' homes are under water?
0.2627 The appropriate Excel function is =NORM.DIST(0.3,0.35,SQRT(0.35*(1-0.35)/30)*SQRT((160-30)/(160-1)),TRUE) = 0.2627
Alison has all her money invested in two mutual funds, A and B. She knows that there is a 40% chance that fund A will rise in price, and a 60% chance that fund B will rise in price given that fund A rises in price. There is also a 20% chance that fund B will rise in price. What is the probability that neither fund will rise in price?
0.64 Given: P(A) = 0.40 and P(B|A) = 0.60, P(B) = 0.20 P(neither) = 1 − P(either) = 1 − (A∪B) = 1 − (0.40 + 0.20 − 0.40 × 0.60) = 1 − 0.36 = 0.64
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.
Suppose that 60% of the students do homework regularly. It is also known that 80% of students who had been doing homework regularly, end up doing well in the course. Only 20% of students who had not been doing homework regularly end up doing well in the course. Given that a student did well in the course, what is the probability that the student had been doing homework regularly?
0.857 P(Homework) = 0.60 P(Well|Homework) = 0.80 P(Well|Not Homework) = 0.20 =0.80×0.60/.80×.60+0.20×(1−0.60)=0.857
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.
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 If the order does not matter, the number of combinations is computed as nCx=n!/(n−x)!x!. In Excel, the function used is =COMBIN(30,5) = 142,506
How many ways can a committee of four students be selected from a 15-member club?
15!/(11! × 4!) The number of combinations is computed as nCx=n!/(n−x)!x!.
Which of the following sets of outcomes described below in I and II represent mutually exclusive events? "You are a freshman"; "You are a senior." "You are a freshman"; "You are an underclassman."
Only I represents mutually exclusive events.
Let A and B be two independent events with P(A) = 0.40 and P(B) = 0.20. Which of the following is correct?
P(A∪B)=0.52 The addition rule is calculated as P(A∪B)=P(A)+P(B)−P(A∩B)P(A∪B)=P(A)+P(B)−P(A∩B) And, for independent events, P(A∩B) = P(A) × P(B) P(A∪B) = 0.40 + 0.20 − 0.40 × 0.20 = 0.52
It is known that the length of a certain product X is normally distributed with μ = 20 inches. How is the probability P(X > 24) related to P(X < 16)?
P(X > 24) is the same as P(X < 16). The normal distribution is symmetric around its mean: P(X < μ) = P(X > μ) = 0.5. If x1 − μ = μ − x2 then P(X > x1) = P(X < x2).
San Francisco 49ers' linebacker Patrick Willis won the Defensive Rookie of the Year Award in 2007 with a total of 174 tackles. Tackles are measured on what kind of a scale? Is a variable measuring the number of tackles considered continuous or discrete?
Ratio scale; discrete
The average time between trades for a high-frequency trading investment firm is 40 seconds. Assume the time between trades is exponentially distributed. What is the probability that the time between trades for a randomly selected trade and the one proceeding it is less than 20 seconds?
The appropriate Excel function is =EXPON.DIST(20,1/40,TRUE) = 0.3935
A random sample of size 100 is taken from a population described by the proportion p = 0.60. The probability that the sample proportion is between 0.55 and 0.62 is ______.
The appropriate Excel function is =NORM.DIST(0.62,0.6,SQRT(0.6*0.4/100),TRUE)-NORM.DIST(0.55,0.6,SQRT(0.6*0.4/100),TRUE) = 0.5047
Super Bowl XLVI was played between the New York Giants and the New England Patriots in Indianapolis. Due to a decade-long rivalry between the Patriots and the city's own team, the Colts, most Indianapolis residents were rooting heartily for the Giants. Suppose that 90% of Indianapolis residents wanted the Giants to beat the Patriots. What is the probability that from a sample of 200 Indianapolis residents, fewer than 170 were rooting for the Giants in Super Bowl XLVI?
The appropriate Excel function is =NORM.DIST(170/200,0.9,SQRT(0.9*(1-0.9)/200),TRUE) = 0.0092
You are planning a May camping trip to Denali National Park in Alaska and want to make sure your sleeping bag is warm enough. The average low temperature in the park for May follows a normal distribution with a mean of 32°F and a standard deviation of 8°F. An inexpensive bag you are considering advertises to be good for temperatures down to 38°F. What is the probability that the bag will not be warm enough?
The appropriate Excel function is =NORM.DIST(38,32,8,TRUE) =0.7734
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.
The appropriate Excel function is =NORM.INV(1-0.1736,25,5) =29.70
The contingency table below provides frequencies for the preferred type of exercise for people under the age of 35, and those 35 years of age or older. Find the probability that an individual prefers biking given that he or she is 35 years old or older.
The contingency table shows frequencies for two qualitative or categorical variables, x and y, where each cell represents a mutually exclusive combination of the pair of x and y values. A more convenient way of calculating relevant probabilities is to convert the contingency table to a joint probability table. P(Biking∣35 years or older)=27/159=0.1698
Which of the following is not a characteristic of a probability density function f(x)?
f(x) is symmetric around the mean.
In general, the null and alternative hypotheses are __________.
mutually exclusive
What is the minimum sample size required to estimate a population mean with 95% confidence when the desired margin of error is E = 1.5? The population standard deviation is known to be 10.75.
n = 198 Sample size =(NORM.S.INV(1-0.05/2)*10.75/1.5)^2 = 197.3016, rounds up to 198.
To test if the mean IQ of employees in an organization is greater than 100, a sample of 30 employees is taken and the value of the test statistic is computed as t29 = 2.42 If we choose a 5% significance level, we __________.
reject the null hypothesis and conclude that the mean IQ is greater than 100 p-value =T.DIST.RT(2.42,29) = 0.0110 Since p-value < 0.05, reject the null hypothesis.
What is the relationship between the standard deviation of the sample mean and the population standard deviation?
se (X ) = σ /√n
In any production process, variations in the quality of the end product are inevitable. Assignable variation refers to ______.
specific events or factors that can usually be identified and eliminated
When conducting a hypothesis test concerning the population mean, and the population standard deviation is unknown, the value of the test statistic is calculated as __________.
tdf=x-m/(s/√n)
It is generally believed that no more than 0.50 of all babies in a town in Texas are born out of wedlock. A politician claims that the proportion of babies born out of wedlock is increasing. When testing the two hypotheses, H0: p ≤ 0.50 and HA: p > 0.50, p stands for __________.
the current proportion of babies born out of wedlock
According to the central limit theorem, the distribution of the sample means is normal if ________.
the sample size n ≥ 30 For any sample size n, the sampling distribution of X is normal if the population X from which the sample is drawn is normally distributed. There is no need for the central limit theorem in these instances. When the underlying distribution is unknown and n ≥ 30, the central limit theorem allows us to assume normality.
The study of statistics is NOT about
the study of mind and consciousness.
Events are collectively exhaustive if _____________.
they contain all outcomes of an experiment
A 90% confidence interval is constructed for the population mean. If a 95% confidence interval had been constructed instead (everything else remaining the same), the width of the interval would have been ________ and the probability of making an error would have been _________.
wider; smaller
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 − 3.50/(.4/√ 3.6) =1.5000
For the sample space S = {apple pie, cherry pie, peach pie, pumpkin pie}, what is the complement of A = {pumpkin pie, cherry pie}?
{apple pie, peach pie} The complement of event A, Ac, is the event consisting of all outcomes in the sample space S that are not in A.
The price to earnings ratio, also called the P/E ratio of a stock, is a measure of the price of a share relative to the annual net income per share earned by the firm. Suppose the P/Es for a firm's common stock during the past four quarters are 10, 12, 15, and 11, respectively. The standard deviation of the P/E ratio over the four quarters is __________.
2.16 First, calculate the sample variance (s2). Standard deviation: s=√s2. Wrong answers include assuming the data points are a population and finding the population standard deviation.
The GPA of accounting students in a university is known to be normally distributed. A random sample of 20 accounting students results in a mean of 2.92 and a standard deviation of 0.16. Construct the 95% confidence interval for the mean GPA of all accounting students at this university.
2.92 ±2.093 ( 0.16 / 20−−√ ) =T.INV(1-0.05/2,20-1) = 2.093
An analyst expects that 20% of all publicly traded companies will experience a decline in earnings next year. The analyst has developed a ratio to help forecast this decline. If the company is headed for a decline, there is a 90% chance that this ratio will be negative. If the company is not headed for a decline, there is only a 10% chance that the ratio will be negative. The analyst randomly selects a company with a negative ratio. Based on Bayes' theorem, the posterior probability that the company will experience a decline is
69%. Given: P(decline) = 0.20 P(negative|decline) = 0.90 (negative|declinec) = 0.10 =0.90×0.20/0.90×.20+.10×(1−0.20)=0.69
Romi, a production manager, is trying to improve the efficiency of his assembly line. He knows that the machine is set up correctly only 60% of the time. He also knows that if the machine is set up correctly, it will produce good parts 80% of the time, but if set up incorrectly, it will produce good parts only 20% 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? (bayes theorem)
86% P(correct) = 0.60 P(good|correct) = 0.80 (good|correctc) = 0.20 =0.80×0.60/.80×.60+.20×(1−0.60)=0.86
An analyst is forecasting net income for Excellence Corporation for the next fiscal year. Her low-end estimate of net income is $250,000, and her high-end estimate is $350,000. 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 $337,500 is ______.
=(350000 − 337500)/(350000 − 250000) =12.5%
Suppose the average price for new cars has a mean of $30,100, a standard deviation of $5,600 and is normally distributed. Based on this information, what interval of prices would we expect at least 95% of new car prices to fall within?
$18,900 to $41,300 The empirical rule dictates that 95% of all observations fall in the interval x−+2s.
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.
In inferential statistics, we calculate statistics of sample data to
- estimate unknown population parameters. - conduct tests about unknown population parameters.
The covariance between the returns of A and B is −0.112. The standard deviation of the rates of return is 0.26 for stock A and 0.81 for stock B. The correlation of the rates of return between A and B is the closest to __________.
-0.53
Professor Elderman has given the same multiple-choice final exam in his Principles of Microeconomics class for many years. After examining his records from the past 10 years, he finds that the scores have a mean of 76 and a standard deviation of 12. Professor Elderman offers his class of 36 a pizza party if the class average is above 80. What is the probability that he will have to deliver on his promise?
0.0228 The appropriate Excel function is =1-NORM.DIST(80,76,12/SQRT(36),TRUE) = 0.0228
The probability P(Z < −1.28) is closest to ______.
0.10
Let the lifetime of a new Jet Ski be represented by a lognormal variable, Y = eX where X is normally distributed. Let the mean of the lifetime of the Jet Ski be six years with a standard deviation of three years. What proportion of the Jet Skis will last nine or more years?
0.1369 The appropriate Excel function is =1-LOGNORM.DIST(9,LN(6^2/SQRT(6^2+3^2)),SQRT(LN(1+3^2/6^2)),TRUE) = 0.1369
The National Center for Education would like to estimate the proportion of students who defaulted on their student loans for the state of Arizona. The total sample size needed to construct a 95% confidence interval for the proportion of student loans in default with a margin of error equal to 4% is ______.
601 Sample size =(NORM.S.INV(1-0.05/2)/0.04)^2*0.5*(1-0.5) = 600.2279, rounds up to 601.
Let P(A)=0.6,P(B)=0.5,and P((A∪B)c)=0.1P(A)=0.6,P(B)=0.5,and P((A∪B)c)=0.1 . Calculate P(A|B)P(A|B)
0.40 P(A∪B) = 1 − 0.10 = 0.90 0.90 = 0.60 + 0.50 − P(A∩B) so P(A∩B) = 0.20 P(A∣B)=P(A∩B)/P(B)=0.20/0.50=0.40
Susan has been on a bowling team for 14 years. After examining all of her scores over that period of time, she finds that they follow a normal distribution. Her average score is 225, with a standard deviation of 13. What is the probability that in a one-game playoff, her score is more than 227?
0.4244 Z = (227−225)/(13/√14) = 0.5756 1 − 0.5756 = 0.4244
Suppose we wish to find the required sample size to find a 90% confidence interval for the population proportion with the desired margin of error. If there is no rough estimate p^ of the population proportion, what value should be assumed for p^ ?
0.50
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. ChocolateVanillaSwirlUnder 25 years old402015At least 25 years old154020 What is the probability a randomly selected customer prefers swirled yogurt or is at least 25 years old?
0.60 A contingency table shows frequencies for two qualitative or categorical variables, x and y, where each cell represents a mutually exclusive combination of the pair of x and y values. A more convenient way of calculating relevant probabilities is to convert the contingency table to a joint probability =15+40+20+15/150=0.60
Sarah's portfolio has an expected annual return at 10%, with an annual standard deviation at 12%. If her investment returns are normally distributed, then in any given year Sarah has an approximate ________.
68% chance that the actual return will fall within −2% and 22% For 68% of the data, it can be calculated by adding and subtracting one standard deviation from the mean.
On average, a certain kind of kitchen appliance requires repairs once every four years. Assume that the times between repairs are exponentially distributed. Which of the following Excel commands computes the probability that the appliance will work no more than three years without requiring repairs?
EXPON.DIST(3,0.25,1) Excel's command EXPON.DIST require three parameters: x value, λ, and true/false value "Cumulative."
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 between $3.70 and $3.90 per gallon?
3.80−3.70/3.80−3.50=0.333.
The mean travel time to work is 25.2 minutes (U.S. Census). Further, suppose that commute time follows a log-normal distribution with a standard deviation of 10 minutes. What is the probability a randomly selected U.S. worker has a commute time of less than 20 minutes?
33.97% The appropriate Excel function is =LOGNORM.DIST(20,LN(25.2^2/SQRT(25.2^2+10^2)),SQRT(LN(1+10^2/25.2^2)),TRUE) = 0.3397
The finite population correction factor for the standard error of the mean should be used when the ratio of the sample size to the size of population exceeds ______.
5% As a general guideline, we use the finite factor correction when the sample constitutes at least 5% of the population, that is, n ≥ 0.05N.
According to the Bureau of Justice Statistics, 10% of persons age 16 or older had been victims of identity theft during the prior 12 months in 2016. What is the minimal sample size of a random sample of persons age 16 or older to generate a normal distribution approximation?
50 The normal distribution approximation is justified when np ≥ 5 and n(1−p) ≥ 5. Since p = 0.1, n = 5/0.1 = 50.
The following data represent the wait time, in minutes, for customers calling Dell technical support. 14 21 37 24 19 12 16 69 13 The upper limit for determining outliers for a box-and-whisker plot is __________.
56 minutes Q1 = 13.5 and Q3 = 30.5. Thus, IQR = 30.5 − 13.5 = 17. Consequently, the upper limit above which data values are considered outliers is Q3 + 1.5 × IQR = 30.5 + (1.5 × 17) = 56 minutes.
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% The average growth rate is defined as Gg=n-1√n/1 −1.
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 For the bell-shaped and symmetrical distribution, the empirical rule dictates that approximately 68% of all observations fall in the interval x+−s.
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. MaleFemaleYes35 20 No 56 76 Given that the respondent is male, the probability that he feels that the idea of killing his own food is appealing is the closest to ____.
A contingency table shows frequencies for two qualitative or categorical variables, x and y, where each cell represents a mutually exclusive combination of the pair of x and y values. A more convenient way of calculating relevant probabilities is to convert the contingency table to a joint probability table.(Yes∣Male)=35/35+56=0.38
Which of the following meets the requirements of a cluster sample?
A population can be divided into 50 city blocks. The sample will include residents from two randomly chosen city blocks. A cluster sample includes observations from randomly selected clusters. In this case, two randomly selected clusters from the 50 city blocks will be used to create the sample.
A family has decided to purchase a Toyota minivan or a Honda minivan.
A union
What is probability?
A value between 0 and 1 assigned to an event that measures the likelihood of its occurrence.
Which of the following statements is FALSE regarding the given curves showing the shapes of the probability density function for various values of mean and standard deviation?
All three curves are depicting a standard normal distribution. A standard normal distribution must have a mean of zero which is not the case for the given curves.
A political reporter announces that there is a 40% chance that the next person to come out of the conference room will be a Republican, since there are 60 Republicans and 90 Democrats in the room.
An empirical probability, as 0.40 represents the relative frequency of Republicans in the room, that is, 60/(60 + 90) = 0.40.
A marketing firm is looking for a candidate with a business degree and at least five years of work experience.
An intersection
Using the central limit theorem, applied to the sampling distribution of the sample proportion, what conditions must be met?
As a general guideline, the normal distribution approximation is justified when np≥5 and n(1−p ) ≥ 5
Professor Elderman has given the same multiple-choice final exam in his Principles of Microeconomics class for many years. After examining his records from the past 10 years, he finds that the scores have a mean of 76 and a standard deviation of 12. What is the probability that a class of 15 students will have a class average greater than 70 on Professor Elderman's final exam?
Cannot be determined. As a general guideline, the normal distribution approximation is justified when n > 30.
What is the difference between Chebyshev's Theorem and the Empirical Rule?
Chebyshev's theorem applies to all data sets, whereas the empirical rule is only appropriate when the data have approximately a symmetric and bell-shaped distribution.
(Excel file) 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 __________.
Class width = (Maximum − Minimum)/(Number of classes) = (91 −21)/5 = 14.00 ≈ 14 (We always round up.)
Sampling is used heavily in manufacturing and service settings to ensure high-quality products. In which of the following areas would sampling be inappropriate?
Custom cabinet making
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?
The appropriate Excel function is =1-NORM.DIST(450,387.2,68.5,TRUE) = 0.1796
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?
The appropriate Excel function is =1-NORM.DIST(9,8,0.6,TRUE) = 0.0478
(Excel file) Consider the following data: 1, 2, 4, 5, 10, 12, 18. The 30th percentile is the closest to __________.
First arrange the data in ascending order. Then find the approximate position of the percentile Lp=(n+1)p/100=. In Excel, the function used is =PERCENTILE.EXC(data,0.30) = 2.8.
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%?
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 waiting time at an elevator is uniformly distributed between 30 and 200 seconds. What is the probability a rider must wait more than 1.5 minutes?
For any subinterval [c, d] of the interval [a, b], probability is computed as P(c≤X≤d)=d−c/b−a (200 − 90)/(200 − 30) =0.6471
Which of the following is an example of quantitative data?
Google's closing stock price today
Which of the following are two-tailed tests?
H0:μ = 10, HA:μ ≠ 10
Professors at a local university earn an average salary of $80,000 with a standard deviation of $6,000. The salary distribution is approximately bell-shaped. What can be said about the percentage of salaries that are at least $74,000?
It is about 84%. Because the data are bell-shaped, we apply the empirical rule. According to the empirical rule, approximately 68% of the observations lie within one standard deviation of the mean: μ+−σ.μ+−σ. As a result, 68% of the data will be within 74,000 and 86,000 and (100 − 68)/2 = 16% will fall above 86,000. Therefore 68 + 16 = 74% will fall above 74,000.
Which of the following scales represents the least sophisticated level of measurement?
Nominal
Which scale of data measurement is appropriate for the names of companies listed on the Dow Jones Industrial Average?
Nominal scale
The graph below shows the population distribution of variable X with expected value µ. Which of the following statements is TRUE regarding the given sampling distribution of the sample mean, X, with different sample size?
The green curve has a smaller sample size than the brown curve. According to the central limit theorem, the sampling distribution of the sample mean is approximately normal when the sample size gets large enough, as is in the case of the brown curve. Therefore, it can be concluded that the green curve has a smaller sample size than the brown curve.
A machine that is programmed to package 1.20 pounds of cereal is being tested for its accuracy in a sample of 36 cereal boxes: the sample mean filling weight is calculated as 1.22 pounds. The population standard deviation is known to be 0.06 pounds. Which of the following conclusions is correct with a 95% confidence level?
The machine is operating properly because the interval contains the target. Lower Limit =1.22-CONFIDENCE.NORM(0.05,0.06,36) = 1.20Upper Limit =1.22+CONFIDENCE.NORM(0.05,0.06,36) = 1.24
Alison has all her money invested in two mutual funds, A and B. She knows that there is a 40% chance that fund A will rise in price, and a 60% chance that fund B will rise in price given that fund A rises in price. There is also a 30% chance that fund B will rise in price. What is the probability that at least one of the funds will rise in price?
The multiplication rule is calculated as P(A∩B) = P(B|A) × P(A). Given: P(A) = 0.40 and P(B|A) = 0.60, P(B) = 0.30 P(A∪B) = 0.40 + 0.30 − 0.40 × 0.60 = 0.46.
The data represents the stock price for Google at the end of the past four quarters. Which of the following types of data best describe these values?
Time series
What is the purpose of calculating a confidence interval?
To provide a range of values that, with a certain measure of confidence, contains the population parameter of interest.
The estimation of which of the following requires sampling?
U.S. unemployment rate
We draw a random sample of size 36 from a population with standard deviation 3.5. If the sample mean is 27, what is a 95% confidence interval for the population mean?
[25.8567, 28.1433] Lower Limit =27-CONFIDENCE.NORM(0.05,3.5,36) = 25.8567 Upper Limit =27+CONFIDENCE.NORM(0.05,3.5,36) = 28.1433
Recently, six single-family homes in San Luis Obispo County in California sold at the following prices (in $1,000s): 549,449,705,529,639,609. Find a 95% confidence interval for the mean sale price in San Luis Obispo County.
[484.63, 674.37] Average =AVERAGE(546,449,705,529,639,609) = 579.5 Standard Deviation =STDEV.S(546,449,705,529,639,609) = 90.403 Lower Limit =579.5-CONFIDENCE.T(0.05,90.403,6) = 484.63 Upper Limit =579.5+CONFIDENCE.T(0.05,90.403,6) = 674.37
A random sample of 150 cast aluminum pots is taken from a production line once every day. The number of defective pots is counted. The proportion of defective pots has been closely examined in the past and is believed to be 0.04. The sample proportions for the week are shown in the accompanying table. Day of the WeekProportion DefectiveMonday0.06Tuesday0.07Wednesday0.04Thursday0.06Friday0.05 Is the production process in control?
Yes, because the sample proportions fall within the upper and lower control limits All sample proportions fall randomly between the lower and upper control limits (1) UCL =0.04+3*SQRT(0.04*(1-0.04)/150) = 0.088 (2) LCL =0.04-3*SQRT(0.04*(1-0.04)/150) = −0.008 ~ 0.00
Is it possible for a data set to have no mode?
Yes, if there are no observations that occur more than once.
Consider the following hypotheses that relate to the medical field: H0: A person is free of disease. HA: A person has disease. In this instance, a Type II error is often referred to as __________.
a false negative A Type II error is made when we do not reject the null hypothesis and the null hypothesis and the null hypothesis is actually false. We often call this type of result a false negative.
In any production process, variation in the quality of the end product is inevitable. Chance variation, or common variation, refers to ______.
a number of randomly occurring events that are part of the production process
subjective probability
drawn on personal judgment
classical probability
based on logical analysis rather than on observation or personal judgment.
Population parameters are difficult to calculate due to
both cost prohibitions on data collection and the infeasibility of collecting data on the entire population.
Time series data refers to
data collected by recording a characteristic of a subject over several time periods.
The two branches of the study of statistics are generally referred to as
descriptive and inferential statistics.
