Liberty University BUSI 230 review and exam 1 complete solutions answers and more!

Liberty University BUSI 230 review and exam 1 complete solutions answers and more!

For the following frequency distribution, how many individual scores are in the entire set?

If all n = 10 individuals in a sample have exactly the same score, what value will have the sample standard deviation?

For the scores shown in the following stem and leaf display, what is the lowest score in the distribution?

For the scores shown in the following stem and leaf display, how many people had scores in the 70s?

Which set of scores has the smallest standard deviation?

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.

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.)

Government agencies carefully monitor water quality and its effect on wetlands (Reference: Environmental Protection Agency Wetland Report EPA 832-R-93-005). Of particular concern is the concentration of nitrogen in water draining from fertilized lands. Too much nitrogen can kill fish and wildlife. Twenty-eight samples of water were taken at random from a lake. The nitrogen concentration (milligrams of nitrogen per liter of water) was determined for each sample.

(a) Identify the variable.

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(b) Is the variable quantitative or qualitative?

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(c) What is the implied population?

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Categorize these measurements associated with a robotics company according to level: nominal, ordinal, interval, or ratio.

(a) Salesperson's performance: below average, average, above average.

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(b) Price of company's stock

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(c) Names of new products

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(d) Temperature (°F) in CEO's private office

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(e) Gross income for each of the past 5 years

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(f) Color of product packaging

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The following data represent glucose blood levels (mg/100 ml) after a 12-hour fast for a random sample of 70 women (Reference: American Journal of Clinical Nutrition, Vol. 19, pp. 345-351).

For this problem, use six classes.

6

(a) Find the class width.

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(b) Make a frequency table showing class limits, class boundaries, midpoints, frequencies, relative frequencies, and cumulative frequencies. (Give relative frequencies to 4 decimal places.)

(c) Draw a histogram.

(d) Draw a relative-frequency histogram.

(e) Categorize the basic distribution shape.

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(f) Draw an ogive. (Graph each point and the closed line segments connecting the points to create your graph.)

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.

Make a stem-and-leaf display of the data for the average length of stay in days. (Use the digit(s) to the left of the decimal point as the stem and the digit to the right as the leaf. Enter NONE in any unused answer blanks.)

Average Length of Hospital Stay

Comment about the general shape of the distribution.

Where does all the water go? According to the Environmental Protection Agency (EPA), in a typical wetland environment, 40% of the water is outflow; 48% is seepage; 4% evaporates; and 8% remains as water volume in the ecosystem (Reference: United States Environmental Protection Agency Case Studies Report 832-R-93-005). Chloride compounds as residuals from residential areas are a problem for wetlands. Suppose that in a particular wetland environment the following concentrations (mg/l) of chloride compounds were found: outflow, 72.3; seepage, 75.6; remaining due to evaporation, 36.6; in the water volume, 50.2.

(a) Compute the weighted average of chlorine compound concentration (mg/l) for this ecological system. (Round your answer to one decimal place.)

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(b) Suppose the EPA has established an average chlorine compound concentration target of no more than 58 mg/l. Does this wetlands system meet the target standard for chlorine compound concentration?

How are dotplots and stem-and-leaf displays similar?

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How are they different?

You are conducting a study of students doing work-study jobs on your campus. Among the questions on the survey instrument are the following.

A. How many hours are you scheduled to work each week? Answer to the nearest hour.

B. How applicable is this work experience to your future employment goals?

Respond using the following scale: 1= not at all, 2 = somewhat, 3 = very

(a) Suppose you take random samples from the following groups: freshmen, sophomores, juniors, and seniors. What kind of sampling technique are you using (simple random, stratified, systematic, cluster, multistage, convenience)?

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(b) Describe the individuals of this study.

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(c) What is the variable for question A?

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Classify the variable as qualitative or quantitative.

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What is the level of measurement?

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(d) What is the variable for question B?

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Classify the variable as qualitative or quantitative.

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What is the level of measurement?

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(e) Is the proportion of responses "3 = very" to question B a statistic or a parameter?

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(f) Suppose only 40% of the students you selected for the sample respond. What is the nonresponse rate?

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Do you think the nonresponse rate might introduce bias into the study? Explain.

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(g) Would it be appropriate to generalize the results of your study to all work-study students in the nation? Explain.

Categorize the type of sampling (simple random, stratified, systematic, cluster, or convenience) used in each of the following situations.

(a) To conduct a preelection opinion poll on a proposed amendment to the state constitution, a random sample of 10 telephone prefixes (first three digits of the phone number) was selected, and all households from the phone prefixes selected were called.

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(b) To conduct a study on depression among the elderly, a sample of 30 patients in one nursing home was used.

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(c) To maintain quality control in a brewery, every 20th bottle of beer coming off the production line was opened and tested.

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(d) Subscribers to a new smart phone app that streams songs were assigned numbers. Then a sample of 30 subscribers was selected by using a random-number table. The subscribers in the sample were invited to rate the process for selecting the songs in the playlist.

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(e) To judge the appeal of a proposed television sitcom, a random sample of 10 people from each of three different age categories was selected and those chosen were asked to rate a pilot show.

Consider these types of graphs: histogram, bar graph, Pareto chart, pie chart, stem-and-leaf display.

(a) Which are suitable for qualitative data? (Select all that apply.)

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(b) Which are suitable for quantitative data? (Select all that apply.)

Describe how data outliers might be revealed in histograms and stem-and-leaf plots.

Driving under the influence of alcohol (DUI) is a serious offense. The following data give the ages of a random sample of 50 drivers arrested while driving under the influence of alcohol. This distribution is based on the age distribution of DUI arrests given in the Statistical Abstract of the United States (112th Edition).

(a) Make a stem-and-leaf display of the age distribution. (Use the tens digit as the stem and the ones digit as the leaf. Enter numbers from smallest to largest separated by spaces. Enter NONE for stems with no values.)

(b) Make a frequency table using seven classes.

(c) Make a histogram showing class boundaries.

(d) Draw a relative frequency histogram.

(e) Identify the shape of the distribution.

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(f) Draw an ogive. (Graph each point and the closed line segments connecting the points to create your graph.)

(g) Discuss how this data might be used to price auto insurance for different age groups.

Describe how the presence of possible outliers might be identified on the following.

(a) histograms

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(b) dotplots

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(c) stem-and-leaf displays

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(d) box-and-whisker plots

Compute the variance and standard deviation for the following population of scores.

Calculate the variance and standard deviation for the following sample of scores

Consider the following ordered data

(a) Find the low, Q1, median, Q3, and high.

(b) Find the interquartile range.

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(c) Make a box-and-whisker plot.

Categorize these measurements associated with fishing according to level: nominal, ordinal, interval, or ratio.

(a) Species of fish caught: perch, bass, pike, trout

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(b) Cost of rod and reel

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(c) Time of return home

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(d) Guidebook rating of fishing area: poor, fair, good

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(e) Number of fish caught

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(f) Temperature of water

How large is a wolf pack? The following information is from a random sample of winter wolf packs. Winter pack size are given below. Compute the mean, median, and mode for the size of winter wolf packs. (Enter your answers to one decimal place.)

Certain kinds of tumors tend to recur. The following data represent the lengths of time, in months, for a tumor to recur after chemotherapy (Reference: D.P. Byar, Journal of Urology, Vol. 10, pp. 556-561).

(a) Make a dotplot for the data above regarding the recurrence of tumors after chemotherapy. Select the appropriate dotplot below.

(b) Compare the dotplot to a histogram of the data. (Select all that apply.)

Modern Managed Hospitals (MMH) is a national for-profit chain of hospitals. Management wants to survey patients discharged this past year to obtain patient satisfaction profiles. They wish to use a sample of such patients. Several sampling techniques are described below. Categorize each technique as simple random sample, stratified sample, systematic sample, cluster sample, or convenience sample.

(a) Obtain a list of patients discharged from all MMH facilities. Divide the patients according to length of hospital stay (2 days or less, 3-7 days, 8-14 days, more than 14 days). Draw simple random samples from each group.

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(b) Obtain lists of patients discharged from all MMH facilities. Number these patients, and then use a random-number table to obtain the sample.

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(c) Randomly select some MMH facilities from each of five geographic regions, and then include all the patients on the discharge lists of the selected hospitals.

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(d) At the beginning of the year, instruct each MMH facility to survey every 500th patient discharged.

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(e) Instruct each MMH facility to survey 10 discharged patients this week and send in the results.

Certain kinds of tumors tend to recur. The following data represent the lengths of time, in months, for a tumor to recur after chemotherapy (Reference: D.P. Byar, Journal of Urology, Vol. 10, pp. 556-561).

For this problem, use five classes.

5

(a) Find the class width.

Answer

(b) Make a frequency table showing class limits, class boundaries, midpoints, frequencies, relative frequencies, and cumulative frequencies. (Give relative frequencies to 2 decimal places.)

(c) Draw a histogram.

(d) Draw a relative-frequency histogram

(e) Categorize the basic distribution shape.

(f) Draw an ogive. (Graph each point and the closed line segments connecting the points to create your graph.)

How long did real cowboys live? One answer may be found in the book The Last Cowboys by Connie Brooks (University of New Mexico Press). This delightful book presents a thoughtful sociological study of cowboys in West Texas and Southeastern New Mexico around the year 1890. A sample of 32 cowboys gave the following years of longevity:

(a) Make a stem-and-leaf display for these data. (Use the tens digit as the stem and the ones digit as the leaf.)

(b) Consider the following quote from Baron von Richthofen in his Cattle Raising on the Plains of North America: "Cowboys are to be found among the sons of the best families. The truth is probably that most were not a drunken, gambling lot, quick to draw and fire their pistols." Does the data distribution of longevity lend credence to this quote?

The archaeological site of Tara is more than 4000 years old. Tradition states that Tara was the seat of the high kings of Ireland. Because of it's archaeological importance, Tara has received extensive study (Reference: Tara: An Archaeological Survey by Conor Newman, Royal Irish Academy, Dublin). Suppose an archaeologist wants to estimate the density of ferromagnetic artifacts in the Tara region. For this purpose, a random sample of 55 plots, each of size 100 square meters, is used. The number of ferromagnetic artifacts for each plot is determined.

(a) Identify the variable.

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(b) Is the variable quantitative or qualitative?

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(c) What is the implied population?

At General Hospital, nurses are given performance evaluations to determine eligibility for merit pay raises. The supervisor rates the nurses on a scale of 1 to 10 (10 being the highest rating) for several activities: promptness, record keeping, appearance, and bedside manner with patients. Then an average is determined by giving a weight of 2 for promptness, 4 for record keeping, 1 for appearance, and 3 for bedside manner with patients. What is the average rating for a nurse with ratings of 5 for promptness, 6 for record keeping, 3 for appearance, and 2 for bedside manner? (Enter your answer to one decimal place.)

An important part of employee compensation is a benefits package, which might include health insurance, life insurance, child care, vacation days, retirement plan, parental leave, bonuses, etc. Suppose you want to conduct a survey of benefits packages available in private businesses in Hawaii. You want a sample size of 100. Some sampling techniques are described below. Categorize each technique as simple random sample, stratified sample, systematic sample, cluster sample, or convenience sample.

(a) Assign each business in the Island Business Directory a number, and then use a random-number table to select the businesses to be included in the sample.

(b) Use postal ZIP Codes to divide the state into regions. Pick a random sample of 10 ZIP Code areas and then include all the businesses in each selected ZIP Code area.

(c) Send a team of five research assistants to Bishop Street in downtown Honolulu. Let each assistant select a block or building and interview an employee from each business found. Each researcher can have the rest of the day off after getting responses from 20 different businesses.

(d) Use the Island Business Directory. Number all the businesses. Select a starting place at random, and then use every 50th business listed until you have 100 businesses.

(e) Group the businesses according to type: medical, shipping, retail, manufacturing, financial, construction, restaurant, hotel, tourism, other. Then select a random sample of 10 businesses from each business type.

Another display technique that is somewhat similar to a histogram is a dotplot. In a dotplot, the data values are displayed along the horizontal axis. A dot is then plotted over each data value in the data set. For more details, view How to Make a Dotplot. The figure below shows a dotplot generated by Minitab for the number of licensed drivers per 1000 residents by state, including the District of Columbia (Source: U.S. Department of Transportation).

(a) From the dotplot, how many states have 600 or fewer licensed drivers per 1000 residents?

(b) About what percentage of the states (out of 51) seem to have close to 800 licensed drivers per 1000 residents? (Round your answer to one decimal place.)

(c) Consider the intervals 550 to 650, 650 to 750, and 750 to 850 licensed drivers per 1000 residents. In which interval do most of these states fall?