Probability and Statistics: Exam 1 (Chapter 1, 2, 3)

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.) 3 11 8 6 8 8 3 5 4 14 4 16 5 5 3 9 8 9

Mean 7.2 Median 7 Mode 8

For the following frequency distribution, how many individual scores are in the entire set? x f 5 2 4 4 3 1 2 3

N=10

Consider the following ordered data. 4 7 7 8 9 9 10 11 12 (a) Find the low, Q1, median, Q3, and high. (b) Find the interquartile range.

(a) low 4 Q1 7 median 9 Q3 10.5 high 12 (b) 3.5

Categorize these measurements associated with fishing according to level: nominal, ordinal, interval, or ratio. (a) Species of fish caught: perch, bass, pike, trout (b) Cost of rod and reel (c) Time of return home (d) Guidebook rating of fishing area: poor, fair, good (e) Number of fish caught (f) Temperature of water

(a) nominal (b) ratio (c) interval (d) ordinal (e) ratio (f) interval

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. (b) Is the variable quantitative or qualitative? (c) What is the implied population?

(a)number of ferromagnetic artifacts per 100 square meters (b)quantitative (C)the entire Tara region

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. (b) Obtain lists of patients discharged from all MMH facilities. Number these patients, and then use a random-number table to obtain the sample. (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. (d) At the beginning of the year, instruct each MMH facility to survey every 500th patient discharged. (e) Instruct each MMH facility to survey 10 discharged patients this week and send in the results.

(a)stratified sample (b)simple random sample (c)cluster sample (d)systematic sample (e)convenience sample

Which set of scores has the smallest standard deviation? Options: 27, 105, 10, 80 5, 11, 42, 22 145, 143, 145, 147 11, 17, 31, 53

145, 143, 145, 147

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

0

For the scores shown in the following stem and leaf display, how many people had scores in the 70s? 9- 3 7 4 8- 9 4 5 7- 7 0 4 2 6- 6 8 5- 1 4

4

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: 58 52 68 86 72 66 97 89 84 91 91 92 66 68 87 86 73 61 70 75 72 73 85 84 90 57 77 76 84 93 58 47 (a) Make a stem-and-leaf display for these data. (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.)

4-7 5-2 7 8 8 6-1 6 6 8 8 7-0 2 2 3 3 5 6 7 8-4 4 4 5 6 6 7 9 9-0 1 1 2 3 7

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 6 for promptness, 4 for record keeping, 2 for appearance, and 9 for bedside manner? (Enter your answer to one decimal place.)

5.7

For the scores shown in the following stem and leaf display, what is the lowest score in the distribution? 9-3 7 4 8-9 4 5 7-7 0 4 2 6-6 8 5-1 4

51

(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?

Yes, these cowboys certainly lived long lives, as evidenced by the high frequency of leaves for stems 7, 8, and 9 (i.e., 70-, 80-, and 90-year-olds).

Calculate the variance and standard deviation for the following sample of scores: 7, 2, 4, 6, 4, 7, 3, 7

variance 4 standard deviation 2