MTH 233 STATISTICS

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1The x-values in the table to the right are the nicotine amounts (in mg) in different 100 mm filtered, non-"light" menthol cigarettes. The y-values are the nicotine amounts (in mg) in different king-size nonfiltered, nonmenthol, and non-"light" cigarettes. If suitable methods of statistics are used, it can be concluded that the average (mean) nicotine amount of the 100 mm filtered, non-"light" menthol cigarettes is less than the average (mean) nicotine amount of the king-size nonfiltered, nonmenthol, and non-"light" cigarettes. Can it be concluded that the first type of cigarette is safe? Why or why not?

Given that the consumption of nicotine is unsafe, can it be concluded that the first type of cigarette is safe?

A.Since the first type of cigarette contains less nicotine than the second type of cigarette, the first type is less safe. However, it can still be concluded that it is safe.

B.Since the first type of cigarette contains less nicotine than the second type of cigarette, the first type is safer. Therefore, it can be concluded that it is safe.

C.Since the first type of cigarette contains less nicotine than the second type of cigarette, the first type is safer. However, it cannot be concluded that it is safe.

D.

Since the first type of cigarette contains less nicotine than the second type of cigarette, the first type is less safe. Therefore, it cannot be concluded that it is safe.

2What does it mean for the findings of a statistical analysis of data to be statistically significant?Choose the correct answer below.

A.The results are very important to the health and well-being of a certain population.

B.The outcome could easily occur by chance.

C.The results do not make enough difference to be of use.

D.The likelihood of getting these results by chance is very small.

3Determine whether the given value is a statistic or a parameter.The mean salary for construction workers is $ 45 comma 000.The mean salary for construction workers is $45,000.Choose the correct answer below.

A.The value is a parameterparameter because it is a numerical measurement describing some characteristic of a population.population.

B.The value is a statisticstatistic

because it is a numerical measurement describing some characteristic of a sample.sample.

C.The value is a statisticstatistic because it is a numerical measurement describing some characteristic of a population.population.

D.The value is a parameterparameter because it is a numerical measurement describing some characteristic of a sample.sample.

4Determine whether the given value is from a discrete or continuous data set.When a car is randomly selected, it is found to have 4 doors4 doors.Choose the correct answer below.

A.A continuouscontinuous data set because there are infinitely many possible values and those values cannot be counted.values cannot be counted.

B.A continuouscontinuous data set because there are infinitely many possible values and thosethere are infinitely many possible values and those values can be counted.values can be counted.

C.The data set is neither continuous nor discrete.

D.A

discretediscrete data set because there are a finite number of possible values.there are a finite number of possible values. nothing

5Determine which of the four levels of measurement (nominal, ordinal, interval, ratio) is most appropriate for the data below.Class times measured in minutesClass times measured in minutesChoose the correct answer below.

A.The ratioratio level of measurement is most appropriate because the data can becan be ordered commaordered, differencesdifferences can becan be foundfound and areand are meaningful commameaningful, and thereand there is ais a naturalnatural startingstarting zerozero point.point.

B.The intervalinterval level of measurement is most appropriate because the data can becan be ordered comma differences left parenthesis obtained by subtraction right parenthesis can be found and are meaningful comma andordered, differences (obtained by subtraction) can be found and are meaningful, and there is no natural starting point.there is no natural starting point.

C.

The ordinalordinal level of measurement is most appropriate because the data can becan be ordered comma but differences left parenthesis obtained by subtraction right parenthesis cannot be found or areordered, but differences (obtained by subtraction) cannot be found or are meaningless.meaningless.

D.The nominalnominal level of measurement is most appropriate because the data cannot becannot be ordered.ordered.

6What is the difference between a random sample and a simple random sample?Choose the correct answer below.

A.With a random sample, each individual has the same chance of being selected. With a simple random sample, all samples of the same size have the same chance of being selected.

B.With a random sample, all samples of the same size have the same chance of being selected. With a simple random sample, each individual has the same chance of being selected.

7Identify the type of sampling used: random, systematic, convenience, stratified, or cluster.To estimate the percentage of defects in a recent manufacturing batch, a quality control manager at SonySony selects every 1313th music CDmusic CD

that comes off the assembly line starting with the secondsecond until she obtains a sample of 6060 music CDsmusic CDs. Which type of sampling is used?

A.Stratified

B.Random

C.Systematic

D.Convenience

E.Cluster

8Identify the class width, class midpoints, and class boundaries for the given frequency distribution.

Daily Low Temperature

(degrees°F)35 dash 3835-3839 dash 4239-4243 dash 4643-4647 dash 5047-50

What is the class width?(Type an integer or a decimal.)What are the class midpoints?(Use ascending order. Type integers or decimals.)What are the class boundaries?

(Use ascending order. Type integers or decimals.)

9Refer to the accompanying data set and use the 30 screw lengths to construct a frequency distribution. Begin with a lower class limit of 2.9702.970 in, and use a class width of 0.010 in. The screws were labeled as having a length of 3 in.3 in. Does the frequency distribution appear to be consistent with the label? Why or why not?LOADING... Click on icon to view the data.Complete the frequency distribution below.Length (in) Frequency

(Type integers or decimals rounded to the nearest thousandth as needed.)Does the frequency distribution appear to be consistent with the label?

A.Yes, because the frequencies are greatest in the classes closest to the labeled size.

B.No, because the screw lengths are off by as much as 0.03 in.

C.Yes, because the screw lengths are no more than .03 in off the labeled size.

D.No, because the class frequencies are not consistent.

10

The histogram to the right represents the weights (in pounds) of members of a certain high-school programmingprogramming team.What is the class width? What are the approximate lower

1051151251351451551651750123456Weight (lbs)FrequencyA histogram with horizontal axis labeled "Weight (pounds)" from 105 to 175 in intervals of 10 and vertical axis labeled "Frequency" from 0 to 6 in intervals of 1 contains seven adjacent vertical bars with heights as follows: 105 to 115, 3; 115 to 125, 4; 125 to 135, 1; 135 to 145, 0; 145 to 155, 2; 155 to 165, 4; 165 to 175, 2.

and upper class limits of the first class?

What is the class width?The class width is (Simplify your answer.)What are the approximate lower and upper class limits of the first class?The approximate lower class limit is The approximate upper class limit is (Simplify your answers.)

11The table provided below shows paired data for the heights of a certain country's presidents and their main opponents in the election campaign. Construct a scatterplot. Does there appear to be a correlation?LOADING... Click the icon to view the data table for election heights.Construct a scatterplot. Choose the correct graph below.

A.160200160200President's heightOpponent's heightA scatterplot with horizontal scale labeled "President's height" from 160 to 200 in intervals of 5 and vertical scale labeled "Opponent's height" from 160 to 200 in intervals of 5 contains the following 16 plotted points, listed here from left to right: (168, 170); (171, 171); (171, 175); (173, 175); (175, 179); (176, 180); (177, 181); (178, 182); (181, 182); (182, 183); (185, 186); (190, 188); (192, 189); (192, 189); (193, 190); (196, 191).

B.160200160200President's heightOpponent's heightA scatterplot with horizontal scale labeled "President's height" from 160 to 200 in intervals of 5 and vertical scale labeled "Opponent's height" from 160 to 200 in intervals of 5 contains the following 16 plotted points, listed here from left to right: (170, 196); (171, 193); (175, 192); (175, 192); (179, 190); (180, 185); (181, 182); (182, 181); (182, 178); (183, 177); (186, 176); (188, 175); (189, 173); (189, 171); (190, 171); (191, 168).

C.160200160200President's heightOpponent's heightA scatterplot with horizontal scale labeled "President's height" from 160 to 200 in intervals of 5 and vertical scale labeled "Opponent's height" from 160 to 200 in intervals of 5 contains the

following 16 plotted points, listed here from left to right: (168, 189); (171, 179); (171, 183); (173, 182); (175, 182); (176, 186); (177, 175); (178, 181); (181, 188); (182, 190); (185, 189); (190, 191); (192, 170); (192, 175); (193, 171); (196, 180).

D.160200160200President's heightOpponent's heightA scatterplot with horizontal scale labeled "President's height" from 160 to 200 in intervals of 5 and vertical scale labeled "Opponent's height" from 160 to 200 in intervals of 5 contains the following 16 plotted points, listed here from left to right: (170, 192); (171, 193); (175, 177); (175, 192); (179, 171); (180, 196); (181, 178); (182, 173); (182, 175); (183, 171); (186, 176); (188, 181); (189, 168); (189, 185); (190, 182); (191, 190).Does there appear to be a correlation between the president's height and his opponent's height?

A.Yes, there appears to be a correlation. As the president's height increases, his opponent's height decreases.

B.Yes, there appears to be a correlation. As the president's height increases, his opponent's height increases.

C.Yes, there appears to be a correlation. The candidate with the highest height usually wins.

D.No, there does not appear to be a correlation because there is no general pattern to the data.

12Construct a scatter diagram using the data table to the right. This data is from a study comparing the amount of tar and carbon monoxide (CO) in cigarettes. Use tar for the horizontal scale and use carbon monoxide (CO) for the vertical scale. Determine whether there appears to be a relationship between cigarette tar and CO.

Construct a scatter diagram.

A.048121620048121620TarCOA scatter diagram with horizontal scale labeled "Tar" from 0 to 20 in intervals of 1 and vertical scale labeled "CO" from 0 to 20 in intervals of 1 contains the following 15 plotted points, listed here from left to right: (1, 15); (2, 10); (5, 15); (6, 7); (8, 13); (10, 3); (11, 7); (11, 15); (14, 1); (14, 16); (15, 10); (15, 11); (15, 14); (16, 18); (18, 10).

B.048121620048121620TarCOA scatter diagram with horizontal scale labeled "Tar" from 0 to 20 in intervals of 1 and vertical scale labeled "CO" from 0 to 20 in intervals of 1 contains the following 15 plotted points, listed here from left to right: (1, 18); (2, 16); (5, 15); (6, 15); (8, 15); (10, 14); (11, 13); (11, 11); (14, 10); (14, 10); (15, 10); (15, 7); (15, 7); (16, 3); (18, 1).

C.048121620048121620TarCOA scatter diagram with horizontal scale labeled "Tar" from 0 to 20 in intervals of 1 and vertical scale labeled "CO" from 0 to 20 in intervals of 1 contains the following 15 plotted points, listed here from left to right: (1, 1); (2, 3); (5, 7); (6, 7); (8, 11); (10, 10); (11, 10); (11, 10); (14, 13); (14, 15); (15, 14); (15, 15); (15, 16); (16, 15); (18, 18).

D.048121620048121620TarCOA scatter diagram with horizontal scale labeled "Tar" from 0 to 20 in intervals of 1 and vertical scale labeled "CO" from 0 to 20 in intervals of 1 contains the following 15 plotted points, listed here from left to right: (1, 1); (3, 2); (7, 5); (7, 6); (10, 10); (10, 11); (10, 11); (11, 8); (13, 14); (14, 15); (15, 14); (15, 15); (15, 16); (16, 15); (18, 18).Is there a relationship between cigarette tar and CO?

A.Yes, as the amount of tar increases the amount of carbon monoxide also increases.

B.No, there appears to be no relationship.

C.Yes, as the amount of tar increases the amount of carbon monoxide decreases.

13

The graph to the right compares teaching salaries of women and men at private colleges and universities. What impression does the graph create? Does the graph depict the data fairly? Ifnot, construct a graph that depicts the data fairly.

Salaries ($)

WomenMen50000600007000080000

What impression does the graph create?

A.The graph creates the impression that men have salaries that are slightly higher than that of women.

B.The graph creates the impression that men and women have approximately the same salaries.

C.The graph creates the impression that men have salaries that are more than twice the salaries of women.

D.The graph creates the impression that women have salaries that are slightly higher than that of men.Does the graph depict the data fairly?

A.No, because the vertical scale does not start at zero.

B.No, because the data are two-dimensional measurements.

C.Yes, because the vertical scale is appropriate for the data.

D.Yes, because the bars accurately represent each average.If the graph does not depict the data fairly, which graph below does?

A.Salaries ($)

WomenMen020000400006000080000

B.Salaries ($)

WomenMen020000400006000080000

C.Salaries ($)

WomenMen52500600006750075000

14Listed below are the annual tuition amounts of the 10 most expensive colleges in a country for a recent year. What does this "Top 10" list tell us about the population of all of that country's college tuitions?$ 53 comma 242$53,242  $ 53 comma 989$53,989  $ 50 comma 891$50,891  $ 53 comma 831$53,831  $ 51 comma 996$51,996   $ 54 comma 293$54,293  $ 51 comma 714$51,714  $ 53 comma 580$53,580  $ 54 comma 293$54,293  $ 51 comma 228$51,228Find the mean, midrange, median, and mode of the data set.The mean of the data set is

$(Round to two decimal places as needed.)The midrange of the data set is $(Round to two decimal places as needed.)The median of the data set is $(Round to two decimal places as needed.)What is (are) the mode(s) of the data set? Select the correct choice below and, if necessary, fill in the answer box within your choice.

A.The mode(s) of the data set is (are) $(Use a comma to separate answers as needed. Round to two decimal places as needed.)

B.There is no mode.What does this "Top 10" list tell us about the population of all the country's college tuitions?

A.All colleges have tuitions around the median.

B.All colleges have tuitions around the midrange.

15Statistics are sometimes used to compare or identify authors of different works. The lengths of the first 10 words in a book by Terry are listed with the first 10 words in a book by David. Find the mean and median for each of the two samples, then compare the two sets of results.Terry: 33 11 66 11David: 33 22 44 11The mean number of letters per word in Terry's book is The median number of letters per word in Terry's book is The mean number of letters per word in David's book is The median number of letters per word in David's book is Compare the two sets of results. Does there appear to be a difference?

A.Yes. Based on the results, words in Terry's book are longer thanlonger than the words in David's book.

B.No. Based on the results, words in Terry's book are the same length as the words in David's book.

C.Yes. Based on the results, words in Terry's book are shorter thanshorter than the words in David's book.

16Use the magnitudes (Richter scale) of the earthquakes listed in the data set below. Find the mean and median of this data set. Is the magnitude of an earthquake measuring 7.0 on the Richter scale an outlier (data value that is very far away from the others) when considered in the context of the sample data given in this data set? Explain.LOADING... Click the icon to view the earthquake Richter scale data.Find the mean and median of the data set using a calculator or similar data analysis technology.The mean of the data set is (Round to three decimal places as needed.)The median of the data set is (Round to three decimal places as needed.)Is the magnitude of an earthquake measuring 7.0 on the Richter scale an outlier when considered in the context of the sample data given?

A.Yes, because this value is very far away from all of the other data values.

B.No, because this value is not very far away from all of the other data values.

C.

No, because this value is not the maximum data value.

D.Yes, because this value is the maximum data value.

17Which of the following is NOT a characteristic of the mean?Choose the correct answer below.

A.The mean takes every data value into account.

B.The mean is relatively reliable.

C.The mean is called the average by statisticians.

D.The mean is sensitive to outliers.

18

Which of the following is always true?Choose the correct answer below.

A.Data skewed to the right have a longer left tail than right tail.

B.For skewed data, the mode is farther out in the longer tail than the median.

C.

In a symmetric and bell-shaped distribution, the mean, median, and mode are the same.

D.The mean and median should be used to identify the shape of the distribution.