Deck 14: The Nature of Statistics

Question 1

Conduct a survey to determine the major worry of school teachers.

Answer 1

Answers will vary.

Question 2

An alpinism club would like to survey its members to determine where to go next summer. ​
Decide on a reasonable means for conducting the survey to obtain the desired information.
​

A) Survey as many alpinism club members as possible about where they want to go in summer.
B) Survey 1000 random people of different age, sex, nationality, and so on.
C) Survey 1000 random people in the street.
D) Survey 1000 persons whose names are chosen from the local telephone directory.
E) All of these are good surveys.

Answer 2

Survey as many alpinism club members as possible about where they want to go in summer.

Question 3

Conduct a survey to determine whether there is a significant correlation between history scores in the 6th grade and amount of TV viewing.

Answer 3

Answers will vary.

Question 4

Suppose that of 80 workers randomly selected and interviewed, 53 were opposed to an increase in Social Security taxes. Would you accept or reject the hypothesis that the majority of workers are opposed to the increase in taxes? ​

A) reject
B) accept

Question 5

The government wants to use a survey to determine the extent of public approval for a adopting new rules of getting the driving license. ​
Decide on a reasonable means for conducting the survey to obtain the desired information.
​

A) Survey inhabitants of the neighbor country by randomly choosing them.
B) Survey as many inhabitants as possible about what they think of this preposition.
C) Survey students of the local college.
D) Ask the opinion of one student, one pensioner, one nurse and one teacher.
E) Ask the opinion of retired professors or inhabitants.

Question 6

The government wants to use a survey to determine the extent of public approval for a adopting new rules of getting the driving license.
​
Decide on a reasonable means for conducting the survey to obtain the desired information.

Question 7

An environmental group wants to use a survey to determine the extent to which its members would be willing to protest a recent decision of the governor of a particular state. Which of the following procedures would be most appropriate for obtaining a statistically unbiased sample? ​

A) Survey a selection of people whose names are randomly chosen from the telephone directory.
B) Have sign-ups for workers to gather signatures at local malls throughout the state.
C) Survey members attending the annual convention of the environmental group.
D) Survey a selection of people whose names are randomly chosen from a list of members of the environmental group.

Question 8

A pet store would like to use a survey to determine which factors are most important to cat owners in determining the brand of cat food that they purchase. ​
Decide on a reasonable means for conducting the survey to obtain the desired information.
​

A) Survey 1000 persons whose names are chosen from the local telephone directory.
B) Survey 1000 cat keepers by randomly choosing from a list of pets keepers.
C) Survey 1000 random people of different age, sex, nationality, and so on.
D) Survey 1000 random people in the street.
E) None of these means are reasonable.

Question 9

Krispy Kreme is considering building a franchise in a particular city. It will use a survey to determine the extent of interest among residents of the city. Which of the following procedures would be most appropriate for obtaining a statistically unbiased sample?

A) Survey a selection of people who are listed on the residential roll sheets of the city.
B) Survey a random selection of customers coming out of other donut shops in the city.
C) Survey a selection of people whose names are randomly chosen from the telephone directory of the target city.
D) Survey a random selection of people whose names are obtained from national sales records of Krispy Kreme customers.
E) none of the above procedures would be most appropriate.

Question 10

A movie theater would like to use a survey to determine which factors are most important to those who come to their theater. Which of the following procedures would be most appropriate for obtaining a statistically unbiased sample? ​

A) Survey a random selection of people passing by the theater in the mall in front of the theater.
B) Survey a random selection of shoppers in the mall.
C) Survey a random selection of people who are leaving the theater after watching a movie.
D) Induce people to answer survey questions by offering discount coupons for various city events, including the movie theater.

Question 11

Conduct a survey to determine whether there is a significant correlation between math scores in the 8th grade and amount of listening to the radio.

A) 1. Do you entrust to your president?
2) Did you vote for him (her)?
B) 1. Where do you usually buy food?
2) How often do you visit big supermarkets?
C) 1. Do you have a pet?
2) What is it?
D) 1. Do you use the internet?
2) Where do you usually use the Internet?
E) 1. What was your math score in the 8th grade?
2) How much time do you spend listening to the radio?

Question 12

A pet store would like to use a survey to determine which factors are most important to cat owners in determining the brand of cat food that they purchase.
​
Decide on a reasonable means for conducting the survey to obtain the desired information.

Question 13

A community will use a survey to determine if its members approve of a new charter.
​
Decide on a reasonable means for conducting the survey to obtain the desired information.

Question 14

Suppose that John hands you a coin to flip and wants to bet on the outcome. Now, John has tried this sort of thing before, and you suspect that the coin is "rigged." You decide to test this hypothesis by taking a sample. You flip the coin twice, and it is heads both times. You say, "Aha, I knew it was rigged!" John replies, "Don't be silly. Any coin can come up heads twice in a row." ​
The following scheme was devised to allow fair results even if the coin is somewhat biased. The coin is flipped twice. If it comes up heads both times or tails both times, it is flipped twice again. If it comes up heads-tails, this will decide the outcome in favor of the first party; and if it comes up tails-heads, this will decide the outcome in favor of the second party. Will this result in a fair toss even if the coins are biased?
​

A) No
B) Yes

Question 15

Sprint would like to take customers from Pacific Bell, one of its competitors in a certain geographical area. Sprint would like to survey Pacific Bell's customers in order to find out which elements of its service are least satisfactory. Which of the following procedures would be most appropriate for obtaining a statistically unbiased sample? ​

A) Survey a random selection of people chosen from a list of Pacific Bell's customers.
B) Survey a random selection of people chosen from a list of Sprint's customers.
C) Place newspaper advertisements seeking survey participants and survey 100 people randomly chosen from those who respond.
D) Call local phone numbers and ask the person who answers if they are satisfied with their phone service.

Question 16

A movie theater would like to use a survey to determine which factors are most important to those who come to their theater. Which of the following procedures would be most appropriate for obtaining a statistically unbiased sample? ​

A) Survey a random selection of people who are leaving the theater after watching a movie.
B) Survey a random selection of shoppers in the mall.
C) Survey a random selection of people passing by the theater in the mall in front of the theater.
D) Induce people to answer survey questions by offering discount coupons for various city events, including the movie theater.
E) None of these is a good measure.

Question 17

Sprint would like to take customers from Pacific Bell, one of its competitors in a certain geographical area. Sprint would like to survey Pacific Bell's customers in order to find out which elements of its service are least satisfactory. What procedure would be most appropriate for obtaining a statistically unbiased sample?

Question 18

Conduct a survey to determine the major worry of school teachers.

A) 1. Do you sometimes feel worry?
2) When do you usually feel worry?
3) What usually appears to be a reason of these feelings?
B) 1. Do you have a pet?
2) What is it?
3) What is it's name?
C) 1. Do you use the internet ?
2) Do you find it expensive?
3) Where do you usually use the internet?
D) 1. Where do you usually buy food?
2) How often do you visit big supermarkets?
3) What is the mean price of your purchase?
E) 1. Do you entrust to your president?
2) Did you vote for him (her)?
3) Can you name his decision, that you don't appreciate?

Question 19

Suppose that John hands you a coin to flip and wants to bet on the outcome. Now, John has tried this sort of thing before, and you suspect that the coin is "rigged." You decide to test this hypothesis by taking a sample. You flip the coin twice, and it is heads both times. You say, "Aha, I knew it was rigged!" John replies, "Don't be silly. Any coin can come up heads twice in a row."
​
The following scheme was devised by mathematician John von Neumann to allow fair results even if the coin is somewhat biased. The coin is flipped twice. If it comes up heads both times or tails both times, it is flipped twice again. If it comes up heads-tails, this will decide the outcome in favor of the first party; and if it comes up tails-heads, this will decide the outcome in favor of the second party. Show that this will result in a fair toss even if the coins are biased.

Question 20

Suppose that of 80 workers randomly selected and interviewed, 47 were opposed to an increase in Social Security taxes. Would you accept or reject the hypothesis that the majority of workers are opposed to the increase in taxes?
​
It will be correct to __________ (accept, reject) the hypothesis.

Question 21

A new computer circuit was tested and the times (in nanoseconds) required to carry out different subroutines were recorded. Find r. Round your answer to four decimal places. ​

A) 0.3051
B) 0.2777
C) 0.9131
D) 0.9601
E) 0.7479

Question 22

Find the cumulative distribution for the table. The number of bedrooms of homes in a certain community is shown on the table below.

A)
B)
C)
D)
E)

Question 23

Find r for the data shown in table. Round your answer to the nearest thousandth.

A) -0.981
B) -0.952
C) -0.932
D) -0.883
E) -0.843

Question 24

Find the mean, median, and mode for the table. The table shows the distribution of households, according to the number of motor vehicles per household.

A) mean is 1.84; median is 2; mode is 2
B) mean is 1.79; median is 0; mode is 4
C) mean is 1.80; median is 1; mode is 1
D) mean is 1.81; median is 2; mode is 2
E) mean is 1.81; median is 3; mode is 2

Question 25

A bank records the number of mortgage applications and its own prevailing interest rate (at the first of the month) for each of 16 consecutive months. Find the best-fitting line for the interest rate (x) and the number of applications (y).

A)
B) ​
C) ​
D) ​
E) ​

Question 26

Match the equation and correlation with a graph.
​ ​

Question 27

Find the regression line for the data points. Round your answer to the nearest hundredth.

A)
B) ​
C) ​
D) ​
E) ​

Question 28

The ages of the runners in a race and their finishing positions are given in the following table. Assuming x is the finish position and y is the person's age, is there a significant correlation between age and finishing position? ​ ​

A) significant at 5%, but not at 1%
B) significant at both 5% and 1%
C) significant at 1%
D) not significant
E) none of these choices

Question 29

Suppose that people's heights (in centimeters) are normally distributed, with a mean of 170 and a standard deviation of 5. We find the heights of 55 people. How many would you expect to be between 170 and 175 cm?

A) 34
B) 19
C) 17
D) 25
E) 23

Question 30

Draw a scatter diagram and find ​r for the data shown in the table.

A) ​
​
B) ​
​
​
C) ​
​
​
D) ​
​
E) ​
​

Question 31

A bank records the number of mortgage applications and its own prevailing interest rate (at the first of the month) for each of 16 consecutive months. Find the best-fitting line for the interest rate (x) and the number of applications (y). Round the coefficients in equation to three decimal places. ​
y' = __________

Question 32

Find the regression line for the data points. Round the coefficients in the equation to the nearest hundredth. ​ __________

Question 33

The ages of the runners in a race and their finishing positions are given in the following table. Assuming x is the finish position and y is the person's age, is there a significant correlation between age and finishing position? ​ Answer significant at 5%, but not at 1%; not significant; or significant at 1%.

Question 34

Find r for the data shown in table. Round your answer to the nearest thousandth. ​
r = __________

Question 35

A bank records the number of mortgage applications and its own prevailing interest rate (at the first of the month) for each of 16 consecutive months. Is there a correlation between the interest rate (x) and the number of applicants (y), and if so, is it significant at the 5% or the 1% significance level? ​ ​ ​

A) -0.652, significant at 5%
B) -0.652, no significant correlation
C) -0.733, significant at 1%
D) -0.587, significant at 5%
E) -0.587, significant at 1%

Question 36

What percent of the total population is found between the mean and the z-score?

A) 17.17%
B) 22.17%
C) 12.17%
D) 11.79%
E) 27.17%

Question 37

Consider a sample of paired data which gives a linear correlation coefficient r. Use the table to determine whether there is a significant linear correlation.
​ ​ ​
The linear correlation is __________ (significant, not significant).

Question 38

Consider a sample of paired data which gives a linear correlation coefficient r. Use the table to determine whether there is a significant linear correlation. ​ ​ ​

A) yes
B) no

Question 39

A bank records the number of mortgage applications and its own prevailing interest rate (at the first of the month) for each of 16 consecutive months. Is there a correlation between the interest rate (x) and the number of applicants (y), and if so, is it significant at the 5% or the 1% significance level? Round your answer to three decimal places.
​ ​ ​
__________, significant at __________%.

Question 40

What percent of the total population is found between the mean and the z-score?

A) 34.38%
B) 34.13%
C) 44.13%
D) 39.13%
E) 19.13%

Question 41

The graph shows the distribution of scores on a 10-point quiz. Which of the following statements is true about the distribution? ​ ​

A) The mean is the same as the mode.
B) The mean is greater than the mode.
C) The mean is less than the mode.

Question 42

Find the range and the standard deviation. ​
Where necessary, the choices are rounded to the nearest hundredth.
​
0, 2, 2, 6, 7, 10, 12, 19
​

A)
B)
C) ​
D) ​
E) ​

Question 43

Find the three measures of central tendency (the mean, median, and mode). ​
0, 1, 1, 5, 8, 10, 11, 132
​

A) mean = 6.5, median = 21, mode = 1
B) mean = 21, median = 6.5, mode = 1
C) mean = 6.5, median = 21, no mode
D) mean = 21, median = 1, no mode
E) mean = 6.5, median = 21, mode = 2

Question 44

Suppose that people's heights (in centimeters) are normally distributed, with a mean of 170 and a standard deviation of 5. We find the heights of 50 people. How many would you expect to be between 160 and 170 cm? Round your answer to the nearest number. ​
__________ people

Question 45

The table shows the distribution of households, according to the number of motor vehicles per household. Find the cumulative distribution.
Find the mean, median, and mode. Round your answers to two decimal places, if required.
the mean is
__________
the median is
__________
the mode is
__________

Question 46

Suppose that, for a certain exam, a teacher grades on a curve. It is known that the mean is 70 and the standard deviation is 8. There are 50 students in the class. What score would be necessary to obtain an A at least?
​ ​
__________ or above

Question 47

Suppose that, for a certain exam, a teacher grades on a curve. It is known that the mean is 50 and the standard deviation is 6. There are 60 students in the class. How many students should receive a C? ​ ​

A) 43
B) 35
C) 37
D) 21
E) 41

Question 48

Suppose the neck size of men is normally distributed, with a mean of 15.5 inches and a standard deviation of 0.5 inch. A shirt manufacturer is going to introduce a new line of shirts. Assume that if your neck size falls between two shirt sizes, you purchase the next larger shirt size. How many shirts of the 17 size should be included in a batch of 1,000 shirts? Round your answer to the nearest number.
Standard Normal Distribution; z-scores __________ shirt(s)

Question 49

Suppose the neck size of men is normally distributed, with a mean of 15.5 inches and a standard deviation of 0.5 inch. A shirt manufacturer is going to introduce a new line of shirts. Assume that if your neck size falls between two shirt sizes, you purchase the next larger shirt size. How many shirts of the 15 size should be included in a batch of 1,000 shirts?

A) 341
B) 131
C) 136
D) 139
E) 146

Question 50

What percent of the total population is found between the mean and the z-score? Round your answer to two decimal places. ​
__________%

Question 51

Suppose that people's heights (in centimeters) are normally distributed, with a mean of 170 and a standard deviation of 5. We find the heights of 60 people. How many would you expect to be taller than 175 cm?

A) 8
B) 6
C) 4
D) 10
E) 20

Question 52

Find the three measures of central tendency (the mean, median, and mode). ​
3, 6, 10, 12, 29
​

A) mean = 10, median = 12, no mode
B) mean = 12, median = 10, no mode
C) mean = 10, median = 12, mode = 12
D) mean = 12, median = 10, mode = 12
E) mean = 10, median = 10, mode = 12

Question 53

Suppose that, for a certain exam, a teacher grades on a curve. It is known that the mean is 55 and the standard deviation is 7. There are 50 students in the class. What score would be necessary to obtain a C? ​ ​

A) 48 or above
B) 62 or above
C) 50 or above
D) 44 or above
E) 42 or above

Question 54

Find the range and the standard deviation. Round your answer to the nearest hundredth. ​
1, 8, 12, 16, 20
​

A)
B)
C) ​
D) ​
E) ​

Question 55

Suppose that, for a certain exam, a teacher grades on a curve. It is known that the mean is 65 and the standard deviation is 6. There are 40 students in the class. How many students should receive a C?
​ ​
__________ students

Question 56

The diameter of an electric cable is normally distributed, with a mean of 0.8 inch and a standard deviation of 0.01 inch. What is the probability that the diameter will exceed 0.82 inch? Round your answer to four decimal places.
Standard Normal Distribution; z-scores

Question 57

The mean is sometimes called the arithmetic mean to distinguish it from other possible means. For example, a different mean, called the harmonic mean (H.M.), is used to average speeds. This mean is defined to be the sum of the reciprocals of all scores divided into the number of scores. For example, the harmonic mean of the numbers 4, 5, 6, 6, 7, 8 is ​ ​
Find the arithmetic mean and the harmonic mean of the numbers 2, 2, 4, 4, 7, 8, 8, 9, 9, and 10.
​
Round your answers to the nearest hundredth.
​

A)
B)
C) ​
D) ​
E) ​

Question 58

Suppose that people's heights (in centimeters) are normally distributed, with a mean of 170 and a standard deviation of 5. We find the heights of 47 people. How many would you expect to be taller than 174 cm? Round your answer to the nearest number. __________ people

Question 59

The number of bedrooms of homes in a certain community is shown on the table. Find the cumulative distribution.
Find the mean, median, and mode. Round your answers to two decimal places, if required.
​
the mean is
__________
the median is
__________
the mode is
__________

Question 60

The diameter of an electric cable is normally distributed, with a mean of 0.9 inch and a standard deviation of 0.02 inch. What is the probability that the diameter will exceed 0.91 inch?

A) 0.1915
B) 0.2785
C) 0.6170
D) 0.3185
E) 0.3085

Question 61

The wages of employees of a small accounting firm are as follows. Draw a line graph that represents the distribution, and the y-axis represent the number. $60000, $14000, $25000, $25000, $16000, $30000,
$18000, $20000, $25000, $30000, $18000, $35000,
$50000
​​

A)
B)
C)
D)
E)

Question 62

A newspaper article discussing whether Social Security could be cut offered the information shown in figure. Use the information in these graphs to answer the question. There seems to be an error in one of the three line graphs. What is it?

A) Only one line at the bottom
B) The line graph at right begins at 1960
C) The line graph at right begins at 50 rather than 0
D) The lines are too close at the top left graph
E) There are no errors

Question 63

The mean is sometimes called the arithmetic mean to distinguish it from other possible means. For example, a different mean, called the harmonic mean (H.M.), is used to average speeds. This mean is defined to be the sum of the reciprocals of all scores divided into the number of scores. For example, the harmonic mean of the numbers 4, 5, 6, 6, 7, 8 is Find the arithmetic mean and the harmonic mean of the numbers 1, 1, 6, 6, 7, 8, 8, 9, 9, and 10.
Round your answers to the nearest tenth.
The arithmetic mean is
__________
The harmonic mean is
__________

Question 64

The amount of electricity used in a typical all-electric home is shown in the circle graph. If, in a certain month, a home used 2,000 kwh (kilowatt-hours), find the amounts of electricity used by the water heater from the graph. ​ ​

A) 2,200 kwh
B) 22,000 kwh
C) 220 kwh
D) 1,818 kwh
E) 182 kwh

Question 65

The wages of employees of a small accounting firm are as follows. $20,000, $25,000, $25,000, $25,000, $30,000, $30,000,
$35,000, $50,000, $60,000, $14,000, $18,000, $16,000,
$18,000
​
Prepare a frequency distribution.
​

A) ​
B) ​
C) ​
D) ​
E) ​

Question 66

The graph shows the distribution of scores on an examination. Decide whether the statement is true.
The mean is greater than the mode. Answer yes or no.

Question 67

The mean is sometimes called the arithmetic mean to distinguish it from other possible means. For example, a different mean, called the geometric mean (G.M.), is used in business and economics for finding average rates of change, average rates of growth, or average ratios. This mean is defined to be the nth root of the product of the numbers. For example, the geometric mean of the numbers 4, 5, and 6 is ​ ​
Find the arithmetic and geometric means for the numbers 2, 4, 6, 7, 7, 8 and 10.
​
Round your answers to the nearest hundredth.
​

A)
B)
C) ​
D) ​
E) ​

Question 68

Consider the graph and statement shown. Is the graph correct or misleading?
​

Question 69

A newspaper article discussing whether Social Security could be cut offered the information shown in figure. Use the information in these graphs to answer the question. There seems to be an error in the pictograph. What is it?

A) The numbers of people are wrong at the each bar
B) Three-dimensional objects are used to represent linear data
C) There are too many colors in the pictograph
D) The pictograph begins at 1970
E) There are no errors

Question 70

The figure shows a line graph. During which month did Herb incur the most expenses?
​

Question 71

Consider the graph and statement shown. Is the graph correct or misleading?

A) The graph is correct.
B) The graph is misleading.

Question 72

Find the three measures of central tendency (the mean, median, and mode).
1, 6, 9, 14, 20
mean =
__________
median =
__________
mode =
__________
​
Answer no mode if needed.

Question 73

Find the three measures of central tendency (the mean, median, and mode). Round your answers to the nearest tenth, if necessary.
0, 2, 2, 6, 8, 10, 11, 33
Answer no mode if needed.
mean =
__________
median =
__________
mode =
__________

Question 74

The wages of employees of a small accounting firm are as follows. Draw a bar graph that represents the distribution. $60000, $14000, $25000, $25000, $16000, $30000,
$18000, $20000, $25000, $30000, $18000, $35000,
$50000
​
​

A)
B)
C)
D)
E)

Question 75

Find the range and the standard deviation (correct to two decimal places, if necessary).
1, 4, 6, 8, 10
range is
__________
deviation is
__________

Question 76

The mean is sometimes called the arithmetic mean to distinguish it from other possible means. For example, a different mean, called the geometric mean (G.M.), is used in business and economics for finding average rates of change, average rates of growth, or average ratios. This mean is defined to be the nth root of the product of the numbers. For example, the geometric mean of the numbers 4, 5, and 6 is Find the arithmetic and geometric means for the numbers 2, 4, 5, 7, 7, 8 and 11.
Round your answers to the nearest hundredth, if necessary.
The arithmetic mean is
__________
The geometric mean is
__________

Question 77

The amount of electricity used in a typical all-electric home is shown in the circle graph. If, in a certain month, a home used 1,200 kwh (kilowatt-hours), find the amounts of electricity used by the water heater, as displayed in the graph.
​ ​
__________ kwh

Question 78

The wages of employees of a small accounting firm are as follows. Draw a stem-and-leaf plot. $14,000, $16,000, $25,000, $25,000, $18,000, $30,000,
$20,000, $25,000, $30,000, $35,000, $18,000, $50,000,
$60,000
​

A)
B)
C)
D)
E)

Question 79

Find the range and the standard deviation. Round to the nearest hundredth, if necessary.
0, 1, 1, 6, 8, 9, 12, 20
range is
__________
deviation is
__________

Question 80

The figure shows a line graph. During which month did Herb incur the most expenses? ​ ​

A) June
B) November
C) December
D) April
E) October