Questions and Answers of Statistical Techniques in Business

For the data given in Table 6.1 calculate the sample statistics $\bar{x}, \bar{y}, S_{x x}, S_{y y}$, and $S_{x y}$.Table 6.1 5 6 8 9 - 234 2 SAT Mathematics Examination Scores (SATM) and
Researchers have collected data from a random sample of six students on the number of hours spent studying for an exam and the grade received on the exam as given in Table 6.5. Using this data,
Does using social media stress you out? A researcher is interested in whether college students who extensively use social media tend to have higher levels of stress. To test this, a sample of nine
Researchers have collected data from a sample of nine individuals on the number of hours of television watched in a day and the age of the individual. They are interested in estimating if age is
Do towns in Massachusetts with higher elevations tend to get more snowfall? To answer this question, a random sample of five towns in Massachusetts, their average yearly snowfall (in inches), and
An organizational psychologist is interested in determining what factors in the workplace are related to employee satisfaction. Survey data were collected from 20 employees regarding measures of
What a difference a single outlier can make! The data set in Table 7.7 presents a collection of ordered pairs $(x, y)$.a. Using Minitab, draw a scatterplot and run a simple linear regression
Can the use of social media stress you out? A researcher is interested in finding out whether college students who extensively use social media tend to have higher levels of stress. To test this, a
A plant manager wants to estimate how the number of units produced at a plant is affected by the number of employees. The data in Table 7.9 gives a random sample of the number of units produced and
Is there a relationship between buying an expensive car and the level of satisfaction with the car? To answer this question, a consumer researcher randomly sampled 15 individuals, asked them about
The correlation inference that was described in this chapter can only test whether a population coefficient of correlation is significantly different from 0 . We may also be interested in testing
If samples are taken from two different populations, we can also test whether the two population coefficients of correlation are significantly different from each other. To do this, we first need to
The data in Table 8.6 gives the amount of credit card debt for a sample of 24 individuals along with their age, education level, and yearly salary.a. Write the population linear regression
Does your age and weight affect your blood pressure? To test this, a medical researcher collected measures of systolic blood pressure (in $\mathrm{mmHg}$, millimeters of mercury), age (in years),
The asking price of a home is influenced by many different factors such as the number of bedrooms, number of bathrooms, square footage, and the lot size. A random sample of 13 recent home sales
What factors influence how much people are willing to spend on a mortgage or rent payment? The data set in Table 8.9 consists of a random sample of 20 residences and it contains measures of the
You may have noticed in the data set in Table 8.9 that many of the variables have missing values. In fact, only eight of the rows have measures on all six predictor variables. Data sets with missing
An island ferry company wants to determine what factors impact the revenue it makes from running its ferry boats to a local island. The passengers are charged to ride the ferry and also for
The data in Figure 9.19 are from running a multiple regression analysis to develop a model that predicts the selling price of homes based on the number of bedrooms, the number of bathrooms, square
A financial advisor wants to determine what factors influence a mutual funds rate of return. A random sample of 1-year return rates (expressed as a percentage) for 78 mutual funds was collected along
Can you predict final examination scores based on the number of hours studying, major, gender, and current GPA? For a random sample of 17 students, their exam grade (on a scale of $0-100$ ), the
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 participants was asked to complete a survey on happiness and a
In problem #1, we used the given sample data to estimate whether there is a difference in happiness scores based on the type of diet. Using Fisher's LSD, describe and interpret any and all
A researcher wants to investigate whether the amount of alcohol consumed by first-year college students has an impact on their grades. To study this, the researcher first categorized alcohol
In problem \#3, we used the given sample data to estimate whether there is a difference in the first-year GPAs based on the amount of alcohol consumed per week. Using Fisher's LSD, describe and
A researcher wants to know if there is a difference in the average number of hours a person sleeps based on four different types of natural sleep supplements (melatonin, herbal tea, tart cherry
In problem \#5, we used the given sample data to estimate whether there is a difference in the mean number of hours slept based on the type of natural supplement used. Using Fisher's LSD, describe
A study was conducted where 36 patients were randomly assigned to use one of the three over-the-counter pain medications and were asked how long the medicine provided pain relief (rounded to the
Is there a difference in the final examination grades for courses that are offered on-ground, online, or as a hybrid class (a hybrid class is half on-ground and half online)? The data provided in
Using the data given in Table 11.3, perform a Wilcoxon signed-rank test manually by completing Table 11.12 .Table 11.3Table 11.12 Amount Spent Per Month (in Dollars) on Car Payments for a Random
The dosages for the supplement melatonin can vary between $1 \mathrm{and} 60 \mathrm{mg}$, where a dosage of $5 \mathrm{mg}$ is a typical starting dosage. A random sample of 15 individuals using
The Wilcoxon signed-rank test can also be used for paired data by testing if the median difference is different from 0 . The data presented in Table 11.14 gives the before and after cholesterol
An educational researcher is interested in whether students do better in online classes as compared to on-ground classes. A random sample of 50 students was randomly assigned to participate in either
A real estate developer wants to estimate if there is a difference in the price per unit for multifamily apartments based on the where the property is located. A random sample of 12 per unit prices
Is there a difference in the yearly cost to service an automobile based on whether it is a luxury car, economy car, sports utility vehicle, or truck? The data given in Table 11.17 represents a random
Is there a difference in the time spent on social media between males and females? The data given in Table 11.18 gives a random sample of 16 males and 16 females who were asked how much time they
A study was conducted where 36 patients were randomly assigned to use one of the three over-the-counter pain medications and were asked how long the medicine provided pain relief (rounded to the
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 participants was asked to complete a survey on happiness and a
An experiment was conducted to estimate if there is a difference in the mean growth rate of grass based on four brands of fertilizer and whether the conditions are full sun or shade. A randomized
The data presented in Table 12.10 gives the lifetime (in hours) of cell phone batteries based on the age of the battery and the capacity of the battery (in milliamps per hour).a. Which is the row
An investor wants to invest in a mutual fund. She is hoping that the long-term trend for the fund will be increasing. She has data on the mutual fund price collected each month for the years 2016 and
A random sample of new home sales (in dollars) for a four-bedroom house with 2.5 bathrooms and a two-car garage based on the age of the home and the region of the United States is given in Table
An educational researcher wants to investigate the tuition patterns at Central Connecticut State University (CCSU). The data in Table 12.13 gives the tuition (in dollars) for full-time undergraduate
The data set in Table 2.9 consists of the profits/losses (in millions of dollars) for a random sample of 20 companies.a. Draw a histogram of the company profits/losses for this sample of companies
Using Minitab and the profit/loss data provided in Table 2.9, create a boxplot. Find the values for $Q_{1}, Q_{2}$, and $Q_{3}$, the upper and lower limits, the upper and lower whiskers, and
You may have heard that most car accidents happen within 25 miles of home. The data provided in Table 2.10 is the mileage away from home for a random sample of 36 car accidents that occurred over the
The data set in Table 2.11 provides the yearly salaries (in thousands) for a sample of 15 executives by education, experience, gender, and type of management training (no training, management
The data set in Table 2.12 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, number of large
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

Showing 1 - 100 of 1090