Liberty University BUSI 230 week 2 exercises 2.2-3.3 complete solutions answers and more!

Liberty University BUSI 230 week 2 exercises 2.2-3.3 complete solutions answers and more!

Question 1

A personnel office is gathering data regarding working conditions. Employees are given a list of five conditions that they might want to see improved. They are asked to select the one item that is most critical to them. Which type of graph, circle graph or Pareto chart, would be the most useful for displaying the results of the survey? Why?

Question 2

Your friend is thinking about buying shares of stock in a company. You have been tracking the closing prices of the stock shares for the past 90 trading days. Which type of graph for the data, histogram or time-series, would be best to show your friend? Why?

Question 3

Commercial dredging operations in ancient rivers occasionally uncover archaeological artifacts of great importance. One such artifact is Bronze Age spearheads recovered from ancient rivers in Ireland. A recent study gave the following information regarding discoveries of ancient bronze spearheads in Irish rivers.

(a) Make a Pareto chart for these data.

(b) Make a circle graph for these data.

Question 4

How does average height for boys change as boys get older? According to Physician's Handbook, the average heights at different ages are in the table below.

Make a time-series graph for average height for ages 0.5 through 12 years.

Question 5

Wetlands offer a diversity of benefits. They provide a habitat for wildlife, spawning grounds for U.S. commercial fish, and renewable timber resources. In the last 200 years, the United States has lost more than half its wetlands. Environmental Almanac gives the percentage of wetlands lost in each state in the last 200 years. For the 30 of the lower 48 states, the percentage loss of wetlands per state is as follows.

Make a stem-and-leaf display of these data. (Use the tens digit as the stem and the ones digit as the leaf. Enter NONE in any unused answer blanks.)

Percent of Wetlands Lost

How are the percentages distributed? Is the distribution skewed? Are there any gaps? (Select all that apply.)

Question 6

The American Medical Association Center for Health Policy Research included data, by state, on the number of community hospitals and the average patient stay (in days) in its publication State Health Care Data: Utilization, Spending, and Characteristics. The data (by state) are shown in the table.

Using the number of hospitals per state listed in the table above, make a stem-and-leaf display for the number of community hospitals per state. (Enter NONE in any unused answer blanks.)

Number of Hospitals per State

Which states have an unusually high number of hospitals? (Select all that apply.)

Question 7

Consider the mode, median, and mean.

(a) Which average represents the middle value of a data distribution?

(b) Which average represents the most frequent value of a data distribution?

(c) Which average takes all the specific values into account?

Question 8

What symbol is used for the arithmetic mean when it is a sample statistic? What symbol is used when the arithmetic mean is a population parameter?

Question 9

Find the mean, median, and mode of the data set.

Question 10

Find the mean, median, and mode of the data set.

Question 11

Consider a data set with at least three data values. Suppose the highest value is increased by 10 and the lowest is decreased by 10.

(a) Does the mean change? Explain.

(b) Does the median change? Explain.

(c) Is it possible for the mode to change? Explain.

Question 12

Consider the following types of data that were obtained from a random sample of 49 credit card accounts. Identify all the averages (mean, median, or mode) that can be used to summarize the data. (Select all that apply.)

(a) Outstanding balance on each account.

(b) Name of credit card (e.g., MasterCard, Visa, American Express, etc.).

(c) Dollar amount due on next payment.

Question 13

Consider the following numbers.

(a) Compute the mode, median, and mean.

(b) If the numbers represented codes for the colors of T-shirts ordered from a catalog, which average(s) would make sense? (Select all that apply.)

(c) If the numbers represented one-way mileages for trails to different lakes, which average(s) would make sense? (Select all that apply.)

(d) Suppose the numbers represent survey responses from 1 to 5, with 1 = disagree strongly, 2 = disagree, 3 = agree, 4 = agree strongly, and 5 = agree very strongly. Which average(s) make sense? (Select all that apply.)

Question 14

In this problem, we explore the effect on the mean, median, and mode of adding the same number to each data value.

Consider the data set

(a) Compute the mode, median, and mean. (Enter your answers to one decimal place.)

(b) Add 7 to each of the data values. Compute the mode, median, and mean. (Enter your answers to one decimal place.)

(c) Compare the results of parts (a) and (b). In general, how do you think the mode, median, and mean are affected when the same constant is added to each data value in a set?

Question 15

In this problem, we explore the effect on the mean, median, and mode of multiplying each data value by the same number. Consider the following data set.

(a) Compute the mode, median, and mean.

(b) Multiply each data value by 2. Compute the mode, median, and mean.

(c) Compare the results of parts (a) and (b). In general, how do you think the mode, median, and mean are affected when each data value in a set is multiplied by the same constant?

(d) Suppose you have information about average heights of a random sample of airline passengers. The mode is 66 inches, the median is 73 inches, and the mean is 70 inches. To convert the data into centimeters, multiply each data value by 2.54. What are the values of the mode, median, and mean in centimeters? (Enter your answers to two decimal places.)

Question 16

How hot does it get in Death Valley? The following data are taken from a study conducted by the National Park System, of which Death Valley is a unit. The ground temperatures (°F) were taken from May to November in the vicinity of Furnace Creek. Compute the mean, median, and mode for these ground temperatures. (Enter your answers to one decimal place.)

Question 17

How old are professional football players? The 11th Edition of The Pro Football Encyclopedia gave the following information. Random sample of pro football player ages in years:

(a) Compute the mean, median, and mode of the ages. (Enter your answers to one decimal place.)

(b) Compare the averages. Does one seem to represent the age of the pro football players most accurately? Explain.

Question 18

In your biology class, your final grade is based on several things: a lab score, scores on two major tests, and your score on the final exam. There are 100 points available for each score. However, the lab score is worth 18% of your total grade, each major test is worth 25%, and the final exam is worth 32%. Compute the weighted average for the following scores: 84 on the lab, 78 on the first major test, 81 on the second major test, and 80 on the final exam.

Question 19

Which average - mean, median, or mode - is associated with the standard deviation?

Question 20

What is the relationship between the variance and the standard deviation for a sample data set?

Question 21

When computing the standard deviation, does it matter whether the data are sample data or data comprising the entire population? Explain.

Question 22

What symbol is used for the standard deviation when it is a sample statistic? What symbol is used for the standard deviation when it is a population parameter?

Question 23

Consider the data set.

(a) Find the range.

(b) Use the defining formula to compute the sample standard deviation s. (Round your answer to two decimal places.)

(c) Use the defining formula to compute the population standard deviation σ. (Round your answer to two decimal places.)

Question 24

Each of the following data sets has a mean of x = 10.

(a) Without doing any computations, order the data sets according to increasing value of standard deviations.

(b) Why do you expect the difference in standard deviations between data sets (i) and (ii) to be greater than the difference in standard deviations between data sets (ii) and (iii)? Hint: Consider how much the data in the respective sets differ from the mean.

Question 25

In this problem, we explore the effect on the standard deviation of adding the same constant to each data value in a data set. Consider the following data set.

(a) Use the defining formula, the computation formula, or a calculator to compute s. (Enter your answer to one decimal place.)

(b) Add 2 to each data value to get the new data set 6, 9, 9, 15, 19. Compute s. (Enter your answer to one decimal place.)

(c) Compare the results of parts (a) and (b). In general, how do you think the standard deviation of a data set changes if the same constant is added to each data value?

Question 26

In this problem, we explore the effect on the standard deviation of multiplying each data value in a data set by the same constant. Consider the data set 8, 16, 12, 16, 8.

(a) Use the defining formula, the computation formula, or a calculator to compute s. (Round your answer to one decimal place.)

(b) Multiply each data value by 4 to obtain the new data set 32, 64, 48, 64, 32. Compute s. (Round your answer to one decimal place.)

(c) Compare the results of parts (a) and (b). In general, how does the standard deviation change if each data value is multiplied by a constant c?

(d) You recorded the weekly distances you bicycled in miles and computed the standard deviation to be s = 2.2 miles. Your friend wants to know the standard deviation in kilometers. Do you need to redo all the calculations?

Given 1 mile ≈ 1.6 kilometers, what is the standard deviation in kilometers? (Enter your answer to two decimal places.)

Question 27

One indicator of an outlier is that an observation is more than 2.5 standard deviations from the mean. Consider the data value 80.

(a) If a data set has mean 70 and standard deviation 5, is 80 a suspect outlier?

(b) If a data set has mean 70 and standard deviation 3, is 80 a suspect outlier?

Question 28

Angela took a general aptitude test and scored in the 86th percentile for aptitude in accounting.

(a) What percentage of the scores were at or below her score?

(b) What percentage were above?

Question 29

One standard for admission to Redfield College is that the student must rank in the upper quartile of his or her graduating high school class. What is the minimal percentile rank of a successful applicant?

Question 30

The town of Butler, Nebraska, decided to give a teacher-competency exam and defined the passing scores to be those in the 70th percentile or higher. The raw test scores ranged from 0 to 100. Was a raw score of 82 necessarily a passing score? Explain.

Question 31

Clayton and Timothy took different sections of Introduction to Economics. Each section had a different final exam. Timothy scored 83 out of 100 and had a percentile rank in his class of 72. Clayton scored 85 out of 100 but his percentile rank in his class was 70. Who performed better with respect to the rest of the students in the class, Clayton or Timothy? Explain your answer.

Question 32

At one hospital there is some concern about the high turnover of nurses. A survey was done to determine how long (in months) nurses had been in their current positions. The responses (in months) of 20 nurses were as follows.

Make a box-and-whisker plot of the data.

Find the interquartile range.

Question 33

What percentage of the general U.S. population have bachelor's degrees? The Statistical Abstract of the United States, 120th Edition, gives the percentage of bachelor's degrees by state. For convenience, the data are sorted in increasing order.

(a) Select the box-and-whisker plot.

(b) Find the interquartile range.

(c) Illinois has a bachelor's degree percentage rate of about 26%. Into what quarter does this rate fall?

Question 34

Some data sets include values so high or so low that they seem to stand apart from the rest of the data. These data are called outliers. Outliers may represent data collection errors, data entry errors, or simply valid but unusual data values. It is important to identify outliers in the data set and examine the outliers carefully to determine if they are in error. One way to detect outliers is to use a box-and-whisker plot. Data values that fall beyond the limits

Lower limit: Q1 − 1.5 ✕ (IQR)

Upper limit: Q3 + 1.5 ✕ (IQR)

where IQR is the interquartile range, are suspected outliers. In the computer software package Minitab, values beyond these limits are plotted with asterisks (*). Students from a statistics class were asked to record their heights in inches. The heights (as recorded) were as follows.

(a) Make a box-and-whisker plot of the data.

(b) Find the value of the interquartile range (IQR).

(c) Multiply the IQR by 1.5 and find the lower and upper limits. (Enter your answers to one decimal place.)

(d) Are there any data values below the lower limit? Above the upper limit? List any suspected outliers. What might be some explanations for the outliers?

Question 35

What percentage of the general U.S. population are high-school dropouts? The Statistical Abstract of the United States, 120th Edition, gives the percentage of high-school dropouts by state. For convenience, the data are sorted in increasing order.

(a) Select the box-and whisker plot.

(b) Find the interquartile range.

(c) Wyoming has a dropout rate of about 7%. Into what quartile does this rate fall?