Questions and Answers of Statistical Techniques in Business

Can exercise improve your mood? A researcher was interested in whether there was a relationship between the number of hours exercised and the mood for a sample of six individuals. These individuals
The data provided in Table 3.14 represents a random sample of the daily rainfall (in inches) over a 1-week period during the summer for a small town in Connecticut. Calculate the mean, median, mode,
The data in Table 3.15 is a random sample of the first-year salaries (in thousands of dollars) for a random sample of ten graduates from a university.a. Calculate the mean first-year salary and the
The data given in Table 3.16 are the speeds (in miles per hour) for a random sample of 12 cars driving down a given section of a highway that has a posted speed limit of 65 miles per hour.a.
Find the value of $z$ using the standard normal table or Minitab such that:a. The area to the right of $z$ is 0.5557 .b. The area to the left of $z$ is 0.0116 .c. The area between $-z$ and
Lifetimes of automobile parts often follow the pattern of a normal distribution. For example, the mean lifetime of car batteries tends to be normally distributed. Suppose that the mean number of
Suppose you have a random variable $Z$ that follows a standard normal distribution, find the following probabilities that correspond to the area under the standard normal curve:a. \(P(Z
Suppose you are given a random variable that has the standard normal distribution.a. Find the value of $z$ such that $5 \%$ of all values of this random variable will be greater.b. Find the value
Grades received on computerized examinations can often be approximated by a normal distribution. Assume that the average grade on a statistics examination is 73.25 points and the standard deviation
Suppose a random variable $X$ has a normal distribution with $\mu=70$ and $\sigma=12$. Using Minitab or the standard normal table, find each of the following probabilities:a. $P(X70)$c. \(P(40
The sticker price for a new luxury SUV is $\$ 93,755$, and most people who are interested in purchasing the vehicle will try to negotiate the price. To help in the negotiation process, there are
Justify whether or not each of the following tables represents the probability distribution of a random variable $X$ : X P(X) -1 -2 72 47 0.26 0.45 -3 0.22 -4 0.07 X P(X) 0.21 0.20 0.22 0.20 0.23
You may have taken classes where the exam grades are scaled. One way to scale grades is to use a normal distribution. Suppose an instructor found the mean exam score of 64 and a standard deviation of
Find the mean, variance, and standard deviation for the following probability distribution for the random variable $X$ : 1 X P(X) 0.20 2 0.27 34 0.19 0.34
For the probability distribution in Exercise 14, find the sampling distribution of the sample mean for all samples of size $n=2$. (Hint: The sample means will be the same as given in Figure 3.7,
Minitab can also be used to create a graphical summary of a given variable. The graphical summary can be found by selecting the Stat menu; under Basic Statisticsa. Using Minitab, create a graphical
Often we may be interested in comparing the amount of variability between two different data sets. This can be done using the sample coefficient of variation $(C O V)$, which is a percentage that
The weighted mean, denoted as $\bar{x}_{w}$ is another measure of central tendency that can be used to assign weights (or measures of influence) to each of the individual observations in a sample.
The trimmed mean can also be a useful measure of center. It is found by trimming off a certain percentage of the smallest and largest observations and then calculating the mean. For instance, we can
The kurtosis of a variable represents a measure of how the distribution of a variable is peaked (in other words, how "sharp" the data set appears when you consider its distribution). The kurtosis can
The skewness of a variable can be used as a measure of how symmetrical a distribution is. If a variable is normally distributed, the skewness will be approximately equal to 0 . If the skewness is
Historically, the average age to get married (for the first time) has been 29 years old. A researcher was interested in whether millennials tend to get married later than did generations of the past.
It has been established that the average time it takes for students to complete a bachelor's degree is approximately 4.8 years. In order to help students graduate earlier, a university wants to
A news organization wants to estimate the wait times to vote in the current election. A reporter asked a random sample of 19 voters how long their wait time was and found their mean wait time to be
Suppose that a bottled water plant wants to determine if the bacteria count in their water supply exceeds the safety threshold of $100 \mathrm{cfu} / \mathrm{mL}$ (colony-forming units per
A machine that makes hose fittings is set for a tolerance of $0.25 \mathrm{~cm}$ (i.e., the standard deviation) and a mean diameter of $12 \mathrm{~cm}$. A random sample of 12 fittings (in
A recent political poll was given to 1,000 likely voters before the presidential election. Of these voters, only 475 said they would vote for the candidate who is currently in office. Determine if
The service department at a car dealership serviced 528 cars over the course of a 1 -week period. These customers were asked to complete a survey regarding their experience with the service
A recent study suggests that more than $80 \%$ of all high school mathematics teachers use calculators in their classroom. To test this theory, a national sample of 1,286 high school mathematics
A weight loss program claims that its clients have lost, on average, more than 40 pounds over the course of a 4 -month period. A random sample of 30 participants in the weight loss program shows an
You may have heard of the Beck Depression Inventory (BDI). This is a 21-question survey where higher total scores are indicative of more severe depressive symptoms. In particular, scores greater than
A machine makes pipe fittings to have a mean length of approximately $2 \mathrm{in}$. and the standard deviation of the lengths must be less than $0.04 \mathrm{in}$. To make sure the machine is
A random sample of 1,463 households across the United States found that 938 of these households watch television on more than one night per week. Find and interpret a $99 \%$ confidence interval
A random sample of 1,463 households across the United States found that the mean amount of television watched per week was $15.36 \mathrm{~h}$, with a standard deviation of $4.27 \mathrm{~h}$.
It has been claimed that most car accidents happen less than 25 miles from home. The data set presented in Table 4.9 gives a random sample of the mileage away from home for 36 car accidents in a
In 2013 , it was found that $10 \%$ of all fatal car crashes were caused by distracted driving. A recent study was done to estimate whether the percentage of fatal car crashes caused by distracted
A manufacturer of wood flooring wants to estimate the mean number of defective floor planks in each box of wood flooring. For a random sample of 12 boxes of planks, find the number of defective
A school district wants to estimate the mean number of snow days that they can expect each year. A sample of the number of snow days taken over the last 10 years is given in Table 4.11.a. Find and
Acidity and alkalinity of soil are typically measured on the $\mathrm{pH}$ scale, which has a range from $0-14$. A pH of 7 is considered neutral, a $\mathrm{pH}$ of $0-7$ is acidic, and a
A machine pours soda into 12-ounce bottles. If the standard deviation of the amount of soda poured exceeds 0.23 ounces, then this is an indication that the machine is not working correctly. To see if
An organizational psychologist developed a 2-week training program in order to improve team behavior in an organization. The program consisted of working with teams to promote a more inclusive and
You may have heard that texting while driving can increase the time taken for you to react to avoid an accident. In order to test this, a university set up a driving simulator where 13 participants
Tire manufacturers are often interested in comparing the wear patterns of their tires with that of the other competitors. One way of comparing the wear patterns is to look at both the mean tread life
Which candidate will win the upcoming presidential election? A survey of 1,300 likely voters found that 652 planned to vote for Candidate A, 600 planned to vote for Candidate $\mathrm{B}$, and the
A new program was created to help people smoke less. Table 5.13 gives the average number of cigarettes smoked (per day) before participating in the program and the average number of cigarettes (per
Table 5.14 gives the yearly starting salaries for male and female bachelor's degree graduates who majored in the social sciences.a. Find and interpret a $99 \%$ confidence interval for the
Can deep-breathing techniques help reduce mathematics anxiety? A researcher was interested in knowing if students who practice deep-breathing techniques tend to have less anxiety toward mathematics.
A random sample of 2,750 students who majored in the social sciences found that 908 defaulted on their student loans, and a random sample of 3,560 students who majored in the physical sciences found
Two different presses are used to press shirts for a laundry service. A random sample of the number of shirts that can be pressed in 5 minutes for each type of press is given in Table 5.16.a. Find
A new small engine claims that it can get more miles per gallon (MPG) than the competitor's model. To verify this claim, a random sample of seven engines of each type are put through a series of
A heating and air-conditioning company wants to estimate the number of emergency service calls they receive during the week and on weekends so as to decide how many technicians to have on call. A
A survey was given to a random sample of $1,650 \mathrm{dog}$ owners and a random sample of 1,300 cat owners. The survey asked if they used flea and tick prevention on their pets. Of the 1,650 dog
A new computer operating system was designed so that it does not need as many updates as the current operating system. A random sample of the number of updates for each operating system over the
A landscaper wants to compare the variability in germination rates between two different brands of grass seed. In order to do this, a random sample of 15 plots of land was planted with each type of
We can also test whether two populations' means differ by some constant, $C$. The procedure is similar to testing whether two population means are different from each other; however, the possible
A survey asked 50 consumers to rate their level of satisfaction with a certain brand of laundry detergent. The responses to the survey were either very satisfied with the detergent, satisfied with
Describe each of the following variables as quantitative or qualitative, discrete or continuous, and classify the scale as nominal, ordinal, interval, or ratio:a. Social security numbersb. IQ scorec.
The partial data set given in Table 1.4 consists of a selection of variables for a ferry company that describe the revenue, time of day the ferry left the dock, number of passengers on the ferry,
Can your diet make you happier? A researcher wants to know if the food you eat has an effect on your happiness. A random sample of 41 adult participants completed a survey on happiness and a
Explain why a random sample is one of the best ways to obtain a sample that is representative of the population.
A stratified random sample can be obtained by first partitioning a population into disjoint groups (or strata) and then taking random samples from each of the strata. For instance, a stratified
In a binomial distribution, n = 8 and π = .30. Find the probabilities of the following events.a. x = 2.b. x ≤ 2 (the probability that x is equal to or less than 2).c. x ≥ 3 (the probability that
Topten is a leading source on energy-efficient products. Their list of the top seven vehicles in terms of fuel efficiency for 2022 includes three Hondas.a. Determine the probability distribution for
In a Poisson distribution μ = 4.a. What is the probability that x = 2?b. What is the probability that x ≤ 2?c. What is the probability that x > 2?
SpaceX is a private company that builds and launches rockets into space. Some are manned, some are not. NASA engineers estimate (through computer simulations and modeling) a probability of 1 in 276
For Exercises 27 through 32, use the following information on food items for the years 2012 and 2022.Compute a simple price index for each of the four items. Use 2012 as the base period.
The 2009 RBC Canadian Open golf tournament was played at the Glen Abbey Golf Club in Oakville, Ontario. During the second round, Leif Olson, Arjun Atwal, Casey Wittenberg, and Briny Baird all aced
For Exercises 27 through 32, use the following information on food items for the years 2012 and 2022.Compute a simple aggregate price index. Use 2012 as the base period. Item Margarine
For Exercises 27 through 32, use the following information on food items for the years 2012 and 2022.Compute the Laspeyres price index for 2022 using 2012 as the base period. Item Margarine
In 2022, sales information shows that 30% of new cars and light trucks in the United States were leased. Zook Motors in Kane, Pennsylvania, sold 40 cars and light trucks last month, 10 of them were
For Exercises 27 through 32, use the following information on food items for the years 2012 and 2022.Compute the Paasche index for 2022 using 2012 as the base period. Item Margarine
For Exercises 27 through 32, use the following information on food items for the years 2012 and 2022.Determine Fisher’s ideal index using the values for the Laspeyres and Paasche indexes computed
For Exercises 33 through 38, use the following information. Betts Electronics purchases three replacement parts for robotic machines used in its manufacturing process. Information on the price of the
For Exercises 39 through 44, use the following price information for selected foods for 2015 and 2022 given in the table.Compute a simple aggregate price index. Use 2015 as the base period.
The following data report total, monthly U.S. gasoline sales in millions of dollars from January 2020 to December 2021. (To find the data, go to the site
Using the following time series data of U.S. new car sales ($ millions), respond to the following items. (The data are sourced from https://www.census.gov/retail/index.html#mrts. Find “Monthly
Consider the variable average ticket sale in the Home Depot data presented here. This variable indicates, for example, that customers spent an average of $39.13 on goods during a store visit in 1993.
Use the variables average ticket sale and number of associates to forecast net sales. Are these two independent variables reasonable predictors of net sales?You will need the help of a software
Liam Chu runs a car wash chain with outlets scattered throughout Chicago. He is concerned that some local managers are giving away free washes to their friends. He decides to collect data on the
Ezra McMahan is the owner of Sharkey Chevy, Buick, GMC. At the start of the year, Ezra instituted a customer opinion program to find ways to improve service. The day after the service is performed,
Refer to the Baseball 2021 data, which includes information on the 2021 Major League Baseball season. The data include the mean player salary since 2010. Plot the information and develop a linear
In a residential section of Southern California, a realtor believes that 80% of one-bedroom apartments rent between $1,950 and $2,450. What is the probability of selecting a random sample of 50
According to an IRS study, 30% of taxpayers can prepare, copy, and electronically file a 1040 tax form between 1.5 and 2.0 hours. A consumer watchdog agency selects a random sample of 25 taxpayers.
Refer to the Baseball 2021 data, which report information on the 30 Major League Baseball teams for the 2021 season.a. At the .10 significance level, is there a difference in the variation in team
Mr. Keagan Profit is studying companies going public for the first time. He is particularly interested in the relationship between the size of the offering and the price per share. a. Determine
Jody’s Florist has 15 delivery trucks, used mainly to deliver flowers and flower arrangements in the Greenville, South Carolina, area. Of these 15 trucks, six have brake problems. Five trucks are
In a Poisson distribution μ = 0.4.a. What is the probability that x = 0?b. What is the probability that x > 0?
General Electric Company (GE) is a high-tech industrial company that operates worldwide through its four industrial segments, Power, Renewable Energy, Aviation, and Healthcare, and its financial
General Electric Company (GE) is a high-tech industrial company that operates worldwide through its four industrial segments, Power, Renewable Energy, Aviation, and Healthcare, and its financial
Johnson & Johnson is the world’s largest and most broadly based healthcare company, with corporate offices in New Brunswick, New Jersey. Its common stock is listed on the New York Stock
Johnson & Johnson is the world’s largest and most broadly based healthcare company, with corporate offices in New Brunswick, New Jersey. Its common stock is listed on the New York Stock
Johnson & Johnson is the world’s largest and most broadly based healthcare company, with corporate offices in New Brunswick, New Jersey. Its common stock is listed on the New York Stock
Johnson & Johnson is the world’s largest and most broadly based healthcare company, with corporate offices in New Brunswick, New Jersey. Its common stock is listed on the New York Stock
Aliyah Edwards is employed by the state bureau of economic development. There is a demand for a leading economic index to review past economic activity and to forecast future economic trends in the
Refer to the Baseball 2021 data. Compute the mean number of home runs per game. To do this, first find the mean number of home runs per team for 2021. Next, divide this value by 162 (a season
In parts a, b, and c, use the t-distribution in Appendix B.5 to determine the margin of error in estimating the population mean with a 95% confidence interval if:a. s = 10 and n = 10.b. s = 10 and n
Ms. Malika Wilson is considering running for mayor of Bear Gulch, Montana. Before completing the petitions, she decides to conduct a survey of voters in Bear Gulch. A sample of 400 voters reveals
Use the t-distribution in Appendix B.5 to determine z-values, using three decimals, for a:a. 95% confidence interval.b. 90% confidence interval.c. 80% confidence interval.Appendix B.5
Dr. Hume is a professor of English. Recently she counted the number of misspelled words in a group of student essays. She noted the distribution of misspelled words per essay followed the normal
Refer to the Baseball 2021 data, which report information on the 30 Major League Baseball teams for the 2021 season. Over the last decade, the mean attendance per team followed a normal distribution

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