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Course: MATH 124, Fall 2008

School: Boise State

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Choice Multiple Questions Descriptive Statistics - Summary Statistics 1. Last year a small statistical consulting company paid each of its five statistical clerks \$22,000, two statistical analysts \$50,000 each, and the senior statistician/owner \$270,000. The number of employees earning less than the mean salary is: (a) 0 (b) 4 (c) 5 (d) 6 (e) 7 2. The following table represents the relative frequency of accidents...

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Choice Multiple Questions Descriptive Statistics - Summary Statistics 1. Last year a small statistical consulting company paid each of its five statistical clerks \$22,000, two statistical analysts \$50,000 each, and the senior statistician/owner \$270,000. The number of employees earning less than the mean salary is: (a) 0 (b) 4 (c) 5 (d) 6 (e) 7 2. The following table represents the relative frequency of accidents per day in a city. Accidents Relative Frequency 0 0.55 1 0.20 2 0.10 3 0.15 4 or more 0 Which of the following statements are true? I. The mean and modal number of accidents are equal. II. The mean and median number of accidents are equal. III. The median and modal number of accidents are equal. (a) I only (b) II only (c) III only (d) I, II and III (e) I, II 1 3. During the past few months, major league baseball players were in the process of negotiating with the team owners for higher minimum salaries and more fringe benefits. At the time of the negotiations, most of the major league baseball players had salaries in the \$100,000 \$150,000 a year range. However, there were a handful of players who, via the free agent system, earned nearly three million dollars per year. Which measure of central tendency of players' salaries, the mean or the median, might the players have used in an attempt to convince the team owners that they (the players) were deserving of higher salaries and more fringe benefits? (a) Not enough information is given to answer the question. (b) Either one, because all measures of central tendency are basically the same. (c) Mean. (d) Median. (e) Both the mean and the median. 4. A financial analyst's sample of six companies' book value were \$25, \$7, \$22, \$33, \$18, \$15. The sample mean and sample standard deviation are (approximately): (a) 20 and 79.2 respectively (b) 20 and 8.9 respectively. (c) 120 and 79.2 respectively. (d) 20 and 8.2 respectively. (e) 120 and 8.9 respectively. 5. A sample of underweight babies was fed a special diet and the following weight gains (lbs) were observed at the end of three month. 6.7 2.7 2.5 3.6 3.4 4.1 4.8 5.9 8.3 The mean and standard deviation are: (a) 4.67, 3.82 (b) 3.82, 4.67 (c) 4.67, 1.95 (d) 1.95, 4.67 (e) 4.67, 1.84 c 2006 Carl James Schwarz 2 6. The effect of acid rain upon the yield of crops is of concern in many places. In order to determine baseline yields, a sample of 13 fields was selected, and the yield of barley (g/400 m2 ) was determined. The output from SAS appears below: QUANTILES(DEF=4) MAX 392 99% Q3 234 95% MED 221 90% Q1 174 10% MIN 161 5% 1% EXTREMES LOW HIGH 161 225 168 232 169 236 179 239 205 392 N MEAN STD DEV SKEW USS CV 13 220.231 58.5721 2.21591 671689 26.5958 SUM WGTS 13 SUM 2863 VAR 3430.69 KURT 6.61979 CSS 41168.3 STD MEAN 16.245 100% 75% 50% 25% 0% 392 392 330 163 161 161 The mean, standard deviation, median, and the highest value are: (a) 220.231 3430.60 50% 225 (b) 220.231 16.245 221 225 (c) 220.231 58.5721 50% 392 (d) 220.231 58.5721 221 392 (e) 220.231 58.5721 234 392 7. The effect of salinity upon the growth of grasses is of concern in many places where excess irrigation is causing salt to rise to the surface. In order to determine baseline yields, a sample of 24 fields was selected, and the biomass of grasses in a standard sized plot was measured (kg). The output from SAS appears below: QUANTILES(DEF=4) MAX 22.6 99% 22.6 Q3 11.45 95% 22.52 MED 8.15 90% 21.8 Q1 3.775 10% 1.6 MIN 0.7 5% 0.77 1% 0.7 RANGE 21.9 Q3-Q1 7.675 EXTREMES LOW HIGH 0.7 15.1 1 19.8 2.2 21.3 2.2 22.3 2.8 22.6 N 24 SUM WGTS 24 100% MEAN 9.09 SUM 218.3 75% STD DEV 6.64 VARIANCE 44.0 50% SKEWNE 0.924 KURTO -0.0209 25% USS 2998 CSS 1012.73 0% CV 72 STD MEAN 1.35 T:MEAN=0 6.7153 PROb>|T| 0.0001 SGN RANK 150 PROb>|S| 0.0001 The mean, standard deviation, tenth percentile, and the highest value are: (a) 9.09 44.0 10% 22.6 (b) 9.09 6.64 1.6 15.1 (c) 9.09 6.64 21.8 15.1 (d) 9.09 6.64 1.6 22.6 (e) 9.09 1.35 21.8 15.1 c 2006 Carl James Schwarz 3 8. The heights in centimeters of 5 students are: 165, 175, 176, 159, 170. The sample median and sample mean are respectively: (a) 170, 169 (b) 170, 170 (c) 169, 170 (d) 176, 169 (e) 176, 176 9. If most of the measurements in a large data set are of approximately the same magnitude except for a few measurements that are quite a bit larger, how would the mean and median of the data set compare and what shape would a histogram of the data set have? (a) The mean would be smaller than the median and the histogram would be skewed with a long left tail. (b) The mean would be larger than the median and the histogram would be skewed with a long right tail. (c) The mean would be larger than the median and the histogram would be skewed with a long left tail. (d) The mean would be smaller than the median and the histogram would be skewed with a long right tail. (e) The mean would be equal to the median and the histogram would be symmetrical. 10. In measuring the centre of the data from a skewed distribution, the median would be preferred over the mean for most purposes because: (a) the median is the most frequent number while the mean is most likely (b) the mean may be too heavily influenced by the larger observations and this gives too high an indication of the centre (c) the median is less than the mean and smaller numbers are always appropriate for the centre (d) the mean measures the spread in the data (e) the median measures the arithmetic average of the data excluding outliers. 11. In general, which of the following statements is FALSE? (a) The sample mean is more sensitive to extreme values than the median. c 2006 Carl James Schwarz 4 (b) The sample range is more sensitive to extreme values than the standard deviation. (c) The sample standard deviation is a measure of spread around the sample mean. (d) The sample standard deviation is a measure of central tendency around the median. (e) If a distribution is symmetric, then the mean will be equal to the median. 12. The frequency distribution of the amount of rainfall in December in a certain region for a period of 30 years is given below: Rainfall (in inches) 2.0 - 4.0 4.0 - 6.0 6.0 - 8.0 8.0 - 10.0 10.0 - 12.0 Number of years 3 6 8 8 5 The mean amount of rainfall in inches is: (a) 7.30 (b) 7.25 (c) 7.40 (d) 8.40 (e) 6.50 13. A consumer affairs agency wants to check the average weight of a new product on the market. A random sample of 25 items of the product was taken and the weights (in grams) of these items were classified as follows: Class Limits 74 - 77 77 - 80 80 - 83 83 - 86 86 - 89 Frequency 3 6 9 3 4 The 3rd quartile of the weight in this sample is equal to: (a) 83.00 (b) 75.00 (c) 83.75 c 2006 Carl James Schwarz 5 (d) 18.75 (e) 84.50 14. A random sample of 40 smoking people is classified in the following table: Ages 10 - 20 20 - 30 30 - 40 40 - 50 50 - 60 Total Frequency 4 6 12 10 8 40 The mean age of this group of people. (a) (b) (c) (d) (e) 4.5 8.0 34.5 38.0 1520.0 15. A frequency distribution of weekly wages for a group of employees is given below: Weekly 50.00 75.00 100.00 125.00 150.00 wages - 75.00 - 100.00 - 125.00 - 150.00 - 175.00 Frequency 10 15 60 40 10 The mean for this group is: (a) (b) (c) (d) (e) \$112.50 \$125.00 \$105.41 \$117.13 \$118.50 16. Consider the following cumulative relative frequency distribution: Less than or equal to 5.0 10.0 15.0 20.0 c 2006 Carl James Schwarz Cum. rel. freq. 0.23 0.34 0.41 1.00 6 If this distribution is based on 800 observations, then the frequency in the second interval is: (a) 34 (b) 272 (c) 80 (d) 88 (e) 456 The following information will be used in the next three questions. A sample of 35 observations were classified as follows: Class 0 - 5 5 -10 10-15 15-20 20-25 25-30 30-35 35-40 Frequency 8 2 6 8 5 5 0 1 17. The class mark of the third class is: (a) 10.0 (b) 12.5 (c) 15.0 (d) 7.5 (e) 17.5 18. The sample mean of the above grouped data is: (a) 14.89 (b) 14.23 (c) 15.35 (d) 15.11 (e) 14.74 19. The 80th percentile of the above grouped data is: (a) 27 (b) 22 c 2006 Carl James Schwarz 7 (c) 19 (d) 23 (e) 24 20. Recently, the City of Winnipeg has been criticized for its excessive discharges of untreated sewage into the Red River. A microbiologist take 45 samples of water downstream from the treated sewage outlet and measures the number of coliform bacteria present. A summary table is as follows: Number of Bacteria 20-30 30-40 40-50 50-60 Number of Samples 5 20 15 5 The 80th percentile is approximately: (a) 45 (b) 47 (c) 80 (d) 48 (e) 36 21. Recently, the City of Winnipeg has been criticized for its excessive discharges of untreated sewage into the Red River. A microbiologist take 50 samples of water downstream from the treated sewage outlet and measures the number of coliform bacteria present. A summary table is as follows: Number of Bacteria 50-60 60-70 70-80 80-90 Number of Samples 5 20 10 15 The mean number of bacteria per sample is: (a) 70 (b) 71 (c) 72 (d) 76 (e) 65 c 2006 Carl James Schwarz 8 22. Using the same data as in the previous question, the 75th percentile is approximately: (a) 76.5 (b) 77.5 (c) 75.0 (d) 78.5 (e) 78.0 23. A sample of 99 distances has a mean of 24 feet and a median of 24.5 feet. Unfortunately, it has just been discovered that an observation which was erroneously recorded as "30" actually had a value of "35". If we make this correction to the data, then: (a) the mean remains the same, but the median is increased (b) the mean and median remain the same (c) the median remains the same, but the mean is increased (d) the mean and median are both increased (e) we do not know how the mean and median are affected without further calculations; but the variance is increased. 24. The term test scores of 15 students enrolled in a Business Statistics class were recorded in ascending order as follows: 4, 7, 7, 9, 10, 11, 13, 15, 15, 15, 17, 17, 19, 19, 20 After the calculating mean, median, and mode, an error is discovered: one of the 15's is really a 17. The measures of central tendency which will change are: (a) the mean only (b) the mode only (c) the median only (d) the mean and mode (e) all three measures 25. Suppose a frequency distribution is skewed with a median of \$75.00 and a mode of \$80.00. Which of the following is a possible value for the mean of distribution? (a) \$86 (b) \$91 (c) \$64 c 2006 Carl James Schwarz 9 (d) \$75 (e) None of these 26. Earthquake intensities are measured using a device called a seismograph which is designed to be most sensitive for earthquakes with intensities between 4.0 and 9.0 on the open-ended Richter scale. Measurements of nine earthquakes gave the following readings: 4.5 L 5.5 H 8.7 8.9 6.0 H 5.2 where L indicates that the earthquake had an intensity below 4.0 and a H indicates that the earthquake had an intensity above 9.0. The median earthquake intensity of the sample is: (a) Cannot be computed because all of the values are not known (b) 8.70 (c) 5.75 (d) 6.00 (e) 6.47 27. Earthquake intensities are measured using a device called a seismograph which is designed to be most sensitive for earthquakes with intensities between 4.0 and 9.0 on the open-ended Richter scale Measurements of ten earthquakes gave the following readings: 4.5 L 5.5 H 8.7 8.9 6.0 H 5.2 7.2 where L indicates that the earthquake had an intensity below 4.0 and a H indicates that the earthquake had an intensity above 9.0. One measure of central tendancy is the x% trimmed mean computed after trimming x% of the upper values and x% of the bottom values. The value of the 20% trimmed mean is: (a) Cannot be computed because all of the values are not known (b) 6.00 (c) 6.60 (d) 6.92 (e) 6.57 28. When testing water for chemical impurities, results are often reported as bdl, i.e., below detection limit. The following are the measurements of the amount of lead in a series of water samples taken from inner city households (ppm). c 2006 Carl James Schwarz 10 5, 7, 12, bdl, 10, 8, bdl, 20, 6. Which of the following is correct? (a) The mean lead level in the water is about 10 ppm. (b) The mean lead level in the water is about 8 ppm. (c) The median lead level in the water is 7 ppm. (d) The median lead level in the water is 8 ppm. (e) Neither the mean nor the median can be computed because some values are unknown. 29. A clothing and textiles student is trying to assess the effect of a jacket's design on the time it takes preschool children to put the jacket on. In a pretest, she timed 7 children as they put on her prototype jacket. The times (in seconds) are provided below. n n 65 43 n 119 39 The n's represent children who had not put the jacket on after 120 seconds (in which case the children were allowed to stop). Which of the following would be the best value to use as the "typical" time required to put on the jacket? (a) The median time, which was 43 seconds. (b) The mean time, which was 66 seconds. (c) The median time, which was 52 seconds. ok (d) The median time, which was 119 seconds. ok (e) The missing times (the n's) mean we can't calculate any useful measures of central tendency. 30. For the following histogram, what is the proper ordering of the mean, median, and mode? Note that the graph is NOT numerically precise only the relative positions are important. c 2006 Carl James Schwarz 11 (a) I = mean II = median III = mode (b) I =mode II = median III = mean (c) I = median II = mean III = mode (d) I = mode II = mean III = median (e) I = mean II = mode III = median 31. The following statistics were collected on two groups of cattle Group A 45 1000 lbs 80 lbs Group B 30 800 lbs 70 lbs sample size sample mean sample std. dev Which of the following statements is correct? (a) Group A is less variable than Group B because Group A's standard deviation is larger. (b) Group A is relatively less variable than Group B because Group A's coefficient of variation (the ratio of the standard deviation to the mean) is smaller (c) Group A is less variable than Group B because the std deviation per animal is smaller. (d) Group A is relatively more variable than Group B because the sample mean is larger. (e) Group A is more variable than Group B because the sample size is larger. 32. "Normal" body temperature varies by time of day. A series of readings was taken of the body temperature of a subject. The mean reading was found to be 36.5C with a standard deviation of 0.3C. When converted to F, the mean and standard deviation are: (F = C(1.8) + 32). (a) 97.7, 32 (b) 97.7, 0.30 (c) 97.7, 0.54 (d) 97.7, 0.97 (e) 97.7, 1.80 33. A scientist is weighing each of 30 fish. She obtains a mean of 30 g and a standard deviation of 2 g. After completing the weighing, she finds that the scale was misaligned, and always under reported every weight by 2 g, i.e. a fish that really weighed 26 g was reported to weigh 24 g. What is mean and standard deviation after correcting for the error in the scale? [Hint: recall that the mean measures central tendency and the standard deviation measures spread.] c 2006 Carl James Schwarz 12 (a) 28 g, 2 g (b) 30 g, 4 g (c) 32 g, 2 g (d) 32 g, 4 g (e) 28 g, 4 g 34. A researcher wishes to calculate the average height of patients suffering from a particular disease. From patient records, the mean was computed as 156 cm, and standard deviation as 5 cm. Further investigation reveals that the scale was misaligned, and that all reading are 2 cm too large, e.g., a patient whose height is really 180 cm was measured as 182 cm. Furthermore, the researcher would like to work with statistics based on metres. The correct mean and standard deviation are: (a) 1.56m, .05m (b) 1.54m, .05m (c) 1.56m, .03m (d) 1.58m, .05m (e) 1.58m, .07m 35. Rainwater was collected in water collectors at thirty different sites near an industrial basin and the amount of acidity (pH level) was measured....

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Boise State - MATH - 124
http:/www.stat.sfu.ca/~cschwarz/MultipleChoice/http:/www2.gsu.edu/~dscbms/ibs/qcontent.html
Boise State - MATH - 124
Multiple Choice Questions Correlation1. A research study has reported that there is a correlation of r = -0.59 between the eye color (brown, green, blue) of an experimental animal and the amount of nicotine that is fatal to the animal when consumed
Boise State - MATH - 124
Multiple Choice Questions Correlation1. A research study has reported that there is a correlation of r = -0.59 between the eye color (brown, green, blue) of an experimental animal and the amount of nicotine that is fatal to the animal when consumed
Boise State - MATH - 124
Multiple Choice Questions Least squares1. Given that we have collected pairs of observations on two variables X and Y , we would consider fitting a straight line with X as an explanatory variable if: (a) the change in Y is an additive constant. (b)
Boise State - MATH - 124
Multiple Choice Questions Least squares1. Given that we have collected pairs of observations on two variables X and Y , we would consider fitting a straight line with X as an explanatory variable if: (a) the change in Y is an additive constant. (b)
Boise State - MATH - 124
Multiple Choice Questions Sampling Distributions1. The Gallup Poll has decided to increase the size of its random sample of Canadian voters from about 1500 people to about 4000 people. The effect of this increase is to: (a) reduce the bias of the e
Boise State - MATH - 124
: REVIEW VOCABULARY Bias A systematic error that tends to cause the ob- servations to deviate in the same direction from the truth about the population whenever a sample or experiment is repeated. 95% confidence interval An interval computed from
Boise State - MATH - 124
we are 95% confident that the interval captures the unknown parameter. Confounding Two variables are confounded when their effects on the outcome of a study cannot be distinguished from each other. Control group A group of experimental subjects tha
Boise State - MATH - 124
Convenience sample A sample that consists of the individuals who are most easily available, such as people passing by in the street. A convenience sample is usually biased. Double-blind experiment An experiment in which neither the experimental sub
Boise State - MATH - 124
Sample proportion The proportion p of the mem- bers of a sample having some characteristic (such as agreeing with an opinion 'poll question). The sample proportion from a simple random sample is used to estimate the corresponding proportion p in the
Boise State - MATH - 124
~ SKillS CH ECK 1. An opinion poll contacts 1161 adults and asks them, &quot;Which political party do you think has better ideas for leading the country in the twenty- first century?&quot; In all, 696 of the 1161 say, &quot;The Democrats.&quot; The sample in this sett
Boise State - MATH - 124
products. Hpw would you label this population in order to use Table 7.1? (a) 001, 002, 003, . . . , 439, 440 (b) 000, 001, 002, . . . , 439, 440 (c) 1, 2, . . . , 439, 440 r 1'; 6. You are using the table of random digits to choose a simple random
Boise State - MATH - 124
10. A clinical trial compares an antidepression medicine with a placebo for relief of chronic &quot; headaches. There are 36 headache patients available to serve as subjects. To choose 18 patients to receive the medicine, you would (a) assign labels 01
Boise State - MATH - 124
- 15. An opinion poll asks a simple random sample of 1000 adults how they view the state of the economy. Suppo.se that 35% of all adults would say &quot;good&quot; if they were asked. In repeated samples, the sample proportion p who say &quot;good&quot; would follow a
Boise State - MATH - 124
20. The sample survey in Exercise 13 actually called 150 students, but 23 of the students refused to say whether they pray. This nonresponse could cause the survey result to be in error. The error due to nonresponse
Boise State - MATH - 124
(a) is in addition to the margin of error foQnd in Exercise 17. (b) is included in the margin of error found in Exercise 17. (c) can be ignored because it isn't random.
Boise State - MATH - 124
EXERCISES . Challenge. Discuss Samp1ing 1. A Gallup poll asked, &quot;Do you think the U.S. should take the leading role in world affairs, take a major role but not the leading role, take a minor role, or take no role at all ig world affairs?&quot; Gallup's
Boise State - MATH - 124
.ion . 5. Highway planners made a main street in a college town one-way. Local businesses were &quot; against the change. The local newspaper invited readers to call a telephone number to record their comments. The next day, the paper reported: Readers
Boise State - MATH - 124
Ashley Oaks Country View Mayfair Village Bay Pointe Country Villa Nobb Hill Beau Jardin Crestview Pemberly Bluffs Del-Lynn Courts Brandon Place Fairington Peppermill Briarwood Fairway Pheasant Run Brownstone Knolls , Richfield Burberry Fowler Sagam
Boise State - MATH - 124
On the Bureau of Labor Statistics Web site, you can find data from this survey on 14,959 people aged 25 to 64 whose highest level of education is a bachelor's degree. Think of these people as a population. (a) In order to select an SRS of these peop
Boise State - MATH - 124
attitudes toward alcohol. You have given every student at the party the same chance to be interviewed: What is that chance? Why is your sample not an SRS? Cautions About Samp1e Surveys . 15. An opinion poll calls 1800 randomly chosen residential t
Boise State - MATH - 124
biological knowledge of each of a group of first- year college students, then divides them into two groups. One group uses the animation, and the other studies the text. The company retests all the students and compares the increase in -understanding
Boise State - MATH - 124
(b) What does &quot;significant&quot; mean in a statistical report? (c) Suggest some confounding variables that might explain why moderate drinkers have lower death rates than nondrinkers. (The study adjusted for these variables.) 22. You can use your comput
Boise State - MATH - 124
of instruction. Then use Table 7.1, starting at line 108, to carry out the randomization. 25. Will people' spend less on health care if their health insurance requires them to pay some part of the cost themselves? An experiment on this issue asked i
Boise State - MATH - 124
attractive? Market researchers prepared ads for athletic shoes announcing different levels of discounts (20%, 40%, or 60%). The student subjects who read the ads were also given &quot;inside information&quot; about the fraction of shoes on sale (50% or 100%).
Boise State - MATH - 124
random digits. Unknown to the researchers, the 6 rats labeled 01 to 06 have a genetic defect that favors ca~aracts. If we simply put rats 01 to 09 in ;c the tea group, the ex:periment would be biased against tea. We can observe how random selectio
Boise State - MATH - 124
earnings. The report says that &quot;for academic year earnings, a statistically significant difference was found between the sexes, with men earning more on the average. No significant difference was found between the earnings of black and white student
Boise State - MATH - 124
37. The Tennessee STAR experiment randomly assigned children to regular or small classes during their first four. years of school. When these children reached high school, 40.2% of blacks from small classes took the ACT or SAT college entrance exam
Boise State - MATH - 124
(a) Let each digit in the table stand for one person in this population. Digits 0 to 5 stand for people who bought a lottery ticket, and 6 to 9 stand for people who did not. Why does looking at one digit from Table 7.1 simulate drawing one person at
Boise State - MATH - 124
out all American teenagers.&quot; Explain how your results agree with this statement. . 45. A telephone survey of 880 randomly selected drivers asked, &quot;Recalling the last 10 traffic lights you drove through, how many of them were red when you entered th
Boise State - MATH - 124
poll's margin of sampling error was plus or minus I four percentage points.&quot; Can we be certain that : between 56% and 64% of all adults believe there is a hell? Explain your answer I .49. A survey of Internet users found that males outnumbered femal