STATS
The relative frequency density for a class is obtained by dividing the:
relative frequency of that class by the class width.
In statistics, a representative sample is a sample that:
represents the characteristics of the population as closely as possible.
A statistical experiment is a process that, when performed:
results in one and only one of many observations.
If you divide the number of elements in a sample with a specific characteristic by the total number of elements in the sample, the dividend is the:
sample proportion.
The sampling distribution is the probability distribution of a:
sample statistic.
The probability distribution of a sample statistic is the:
sampling distribution of that statistic.
An error that occurs because of chance is called:
sampling error.
The mean age of all students at a university is 24 years. The mean age of a random sample of 100 students selected from this university is 23.6 years. The difference (23.6 - 24 = -0.4) is the:
sampling error.
The mean weekly earnings of all employees of a company are $822. The mean weekly earnings of a random sample of 25 employees selected from this company is $837. The difference ($837 - $822 = $15) is the:
sampling error.
Two students are randomly selected from a statistics class, and it is observed whether or not they suffer from math anxiety. List all the outcomes included in the following event. Indicate whether this event is simple or compound: "the first student does not suffer and the second suffers from math anxiety".
simple
You toss a coin nine times and observe 2 heads and 7 tails. This event is a:
simple event.
A continuous random variable x has a left-skewed distribution with a mean of 130 and a standard deviation of 22. The sampling distribution of the sample mean for a sample of 16 elements taken from this population is:
skewed to the left.
A continuous random variable x has a right-skewed distribution with a mean of 45 and a standard deviation of 6. The sampling distribution of the sample mean for a sample of 25 elements taken from this population is:
skewed to the right.
When the sample size is greater than 1, the standard deviation of the sampling distribution of the sample means is always:
smaller than the standard deviation of the population.
The standard deviation of a binomial distribution is equal to:
square root of npq.
For the standard normal distribution, the z value gives the distance between the mean and a point in terms of the:
standard deviation.
When a person makes an educated guess about the likelihood that an event will occur, it is an example of
subjective probability..
The mean of a data set is the:
sum of all values divided by the number of values.
Two complementary events
taken together include all outcomes for an experiment.
A conditional probability is a probability
that an event will occur given that another event has already occurred.
A continuous random variable is a random variable:
that can assume any value in one or more intervals.
The sampling error is:
the difference between the value of a sample statistic and the value of the corresponding population parameter.
The mean of the sampling distribution of the sample mean is the mean of:
the means of all possible samples of the same size taken from the population.
Under descriptive statistics, we study
the methods for organizing, displaying, and describing data
Under inferential statistics, we study
the methods to make decisions about one or more populations based on sample results
According to the relative frequency concept of probability, the probability of an event is
the number of times the given event is observed divided by the total number of repetitions of the experiment.
The hypergeometric probability distribution can be used whenever:
the population is finite and sampling occurs without replacement.
In general, "n factorial" represents:
the product of all integers from n to 1.
The measurement units of the standard deviation are always:
the same as those of the original data.
A rectangular histogram has:
the same frequency for each class
The standard deviation of the sampling distribution of the sample proportion is equal to:
the square root of pq/n.
For a normal distribution, the spread of the curve decreases and its height increases as:
the standard deviation decreases.
If a distribution is symmetric with one peak, then:
the values of the mean, median, and mode are identical.
For a normal curve, changing the mean from 34 to 44 will cause the curve to shift
to the right.
In binomial experiments, the outcome called a "success" is an outcome:
to which the question refers.
An observation is a:
value of a variable for a single element.
The median of a data set is the:
value of the middle term in a ranked data set.
A discrete random variable is a random variable:
whose set of values is countable.
The Ohio lottery involves selecting 4 numbers from 4 different bins with the same set of numbers. This is an example of sampling
with replacement..
The Minnesota lottery involves selecting 5 numbers from a single bin. This is an example of sampling
without replacement..
The margin of error for the population mean, assuming σ is known, is:
z multiplied by the standard deviation of the sample mean.
For the standard normal distribution, the mean is:
zero and the standard deviation is 1.
The parameter(s) of the Poisson probability distribution is(are):
λ
The parameters of the normal distribution are:
μ and σ.
The standard deviation of the sampling distribution of the sample mean for a sample size of n drawn from a population with a mean of μ and a standard deviation of σ is:
σ / sqrt of n
Which of the following is true for the probability distribution of a discrete random variable x?
∑Px=1.
The formula used to obtain the mean of a discrete random variable is:
∑xP(x).
The confidence level of an interval estimate is denoted by:
(1−α)×100%.
The correct formula for the limits of a confidence interval for μ is:
(x¯−margin of error,x¯+margin of error).
These data give the times (in minutes) taken to commute from home to work for 20 workers. 10 50 66 334 8 5 11 23 39 26 26 8 17 32 15 19 29 41 21 22 Construct a stem-and-leaf display for these data. Arrange the leaves for each stem in increasing order. Choose the correct display from the list. (Note: To prepare a stem-and-leaf display, each number in this data set can be written as a two-digit number. For example, 5 can be written as 05, for which the stem is 0 and the leaf is 5.)
0 | 5 8 1 | 0 1 5 7 9 2 | 1 2 3 6 6 9 3 | 2 3 9 4 | 1 8 5 | 0 6 | 6
Create a dotplot for the following data set. 1 2 0 5 2 1 3 2 0 5 2 1 2 1 2 0 1 3 1 2
0(3), 1(6), 2(7), 3(2), 4(0), 5(2)
You grab two books at random off a shelf. Let X be the number of those two books that you have previously read. Determine all possible values for the random variable X.
0, 1, 2
Find the area under the standard normal curve between z=0.87 and z=1.78.Round your answer to four decimal places.
0.1547
Which of the following is true for the probability of a discrete random variable x?
0≤Px≤1.
Indicate which of the following are time-series data. 1. Food bill of a family for each month of 2015. 2. Gross sales of 200 ice cream parlors in July 2015. 3. Average prices of houses in 100 cities. 4. Salaries of 50 employees. 5. Number of supermarkets in each of 40 cities as of December 31, 2015.
1
Indicate which of the following variables are discrete. 1. Number of persons in a family. 2. Monthly TV cable bills. 3. Lottery revenues of states. 4. Percentage of sugar in a juice. 5. Number of cars owned by families.
1 and 5
Indicate which of the following variables are continuous. 1. Number of persons in a family. 2. Monthly TV cable bills. 3. Number of typographical errors in newspapers. 4. Percentage of sugar in a juice. 5. Number of cars owned by families.
1, 2, 3, and 4
Indicate which of the following variables are qualitative. 1. Color of cars. 2. Marital status of a person. 3. Number of students in a class. 4. Lottery winners by state. 5. Number of cars owned by families.
1, 2, and 4
Indicate which of the following variables are quantitative. 1. Number of persons in a family. 2. Marital status of a person. 3. Spring break locations favored by college students. 4. Number of typographical errors in newspapers. 5. Number of cars owned by families.
1, 4, and 5
The z value for a 85% confidence interval for the population mean with σ known is:
1.44
The value of t for 19 degrees of freedom and a 90% confidence interval is:
1.729.
The z value for a 92% confidence interval for the population mean with σ known is:
1.75.
The value of t for 15 degrees of freedom and a 90% confidence interval is:
1.753
The z value for a 95% confidence interval for the population mean with σ known is:
1.96
A population consists of five elements: 5, 6, 8, 10, and 13. You choose a random sample of three elements from this population (without replacement). Which of the following is not a possible value of the sample mean?
10.67.
We use the t distribution to make a confidence interval for the population mean if the population from which the sample is drawn is (approximately) normally distributed, the population standard deviation is unknown, and the sample size is at least:
2.
The z value for a 98% confidence interval for the population mean with σ known is:
2.33.
The value of t for 17 degrees of freedom and a 98% confidence interval is:
2.567.
Consider the following stem-and-leaf display. 2-3 | 18 45 55 * 39 67 83 97 4-5 | 07 27 33 71 * 27 37 51 63 81 92 6-8 | 22 36 47 55 78 82 * * 22 46 Write the data set that is represented by this display.
218, 245, 255, 339, 367, 383, 397, 407, 427, 433, 471, 527, 537, 551, 563, 581, 592, 622, 636, 647, 655, 678, 682, 822, 846
The following data give the times (in minutes) taken by 50 students to complete a statistics examination that was given a maximum time of 75 minutes to finish. 41 28 45 59 53 69 70 51 63 68 37 44 42 38 74 53 66 65 52 64 26 45 66 34 43 44 39 55 64 54 38 52 58 72 67 65 43 65 68 27 64 50 71 75 45 69 56 73 53 72 Create a dotplot for these data.
26(1), 27(1), 28(1), 34(1), 37(1), 38(2), 39(1), 41(1), 42(1), 43(2), 44(2), 45(3), 50(1), 51(1), 52(2), 53(3), 54(1), 55(1), 56(1), 58(1), 59(1), 63(1), 64(3), 65(3), 66(2), 67(1), 68(2), 69(2), 70(1), 71(1), 72(2), 73(1), 74(1), 75(1)
The mean age of five members of a family is 40 years. The ages of four of the five members are 61, 52, 27, and 26. The age of the fifth member is:
34.
The mean age of five members of a family is 40 years. The ages of four of the five members are 61, 50, 27, and 23. The age of the fifth member is:
39
Consider the following stem-and-leaf display 4 | 1 7 5 | 0 1 4 7 6 | 2 4 6 7 7 7 8 9 7 | 2 2 3 5 6 6 9 8 | 5 7 8 9 Write the data set that is represented by the display.
41 47 50 51 54 57 62 64 66 67 67 67 68 69 72 72 73 75 76 76 79 85 87 88 89
You want to estimate the amount of arsenic in a well to within 2 milligrams per liter. From previous work, you know that the level varies with σ=5 milligrams per liter. If you want to be 99% certain, how many samples do you need to take?
42 samples
According to the empirical rule, the percentage of values that fall outside two standard deviations of the mean is approximately:
5%.
The value of the 55th percentile for a data set is 52. This means that:
55% of the values in that data set are smaller than 52..
According to Chebyshev's theorem, the minimum percentage of values that fall within 1.5 standard deviations of the mean is:
55.56%.
According to the empirical rule, the percentage of values that fall within one standard deviation of the mean is approximately:
68%.
The following data give the one-way commuting times (in minutes) from home to work for a random sample of 50 workers. 23 17 34 26 18 33 45 42 12 37 44 15 22 19 28 32 18 39 40 48 16 11 9 24 18 26 31 7 30 15 18 22 29 32 30 21 19 14 26 38 25 36 23 41 43 46 29 17 24 31 Create a dotplot for these data.
7(1), 9(1), 11(1), 12(1), 14(1), 15(2), 16(1), 17(2), 18(4), 19(2), 21(1), 22(2), 23(2), 24(2), 25(1), 26(3), 28(1), 29(2), 30(2), 31(2), 32(2), 33(1), 34(1), 36(1), 37(1), 38(1), 39(1), 40(1), 41(1), 42(1), 43(1), 44(1), 45(1), 46(1), 48(1)
The mean score of 15 male students taking a test is 70 and the mean score of 12 female students taking the same test is 77. The combined mean score of the 27 male and female students is
73.11.
The mean score of 15 male students taking a test is 68 and the mean score of 12 female students taking the same test is 83. The combined mean score of the 27 male and female students is
74.67.
According to Chebyshev's theorem, the minimum percentage of values that fall within 2 standard deviations of the mean is:
75%
The mean age of all high school teachers in New York state is 44 years and the standard deviation is 4 years. According to Chebyshev's theorem, the percentage of teachers in New York who are 36 to 52 years old is at least:
75.00.
The percentile rank of a value in a data set is 78. This means that:
78% of the values in that data set are smaller than that value.
The experiment of tossing a coin 3 times has
8 outcomes.
According to Chebyshev's theorem, the minimum percentage of values that fall within 2.5 standard deviations of the mean is:
84.00%.
A box contains a few red, a few black, and a few white marbles. Two marbles are randomly drawn from this box and the color of these marbles is observed. The total number of outcomes for this experiment is
9.
According to the empirical rule, the percentage of values that fall within two standard deviations of the mean is approximately:
95%.
The ages of all high school teachers in New York state have a bell-shaped distribution with a mean of 43 years and a standard deviation of 7 years. According to the empirical rule, the percentage of teachers in this state who are 29 to 57 years old is approximately:
95%.
The ages of all high school teachers in New York state have a bell-shaped distribution with a mean of 45 years and a standard deviation of 7 years. According to the empirical rule, the percentage of teachers in this state who are 24 to 66 years old is approximately:
99.7%.
Find the area under the standard normal curve between z=-2.34 and z=-0.48.Round your answer to four decimal places.
A = 0.3060
Find the area under the standard normal curve between z=-2.01 and z=0.Round your answer to four decimal places.
A = 0.4778
Find the area under the standard normal curve between z=0 and z=2.05.Round your answer to four decimal places.
A = 0.4798
For a standard normal distribution, find the area within 2 standard deviations of the mean, that is, the area between μ-2σ and μ+2σ. Round your answer to four decimal places.
A = 0.9544
A statistical experiment has eight equally likely outcomes that are denoted by 1,2,3,4,5,6,7, and 8. Let event A={1,4,7,8} and event B={3,6,7}. What are the complements of events A and B , and their probabilities?
A = {2,3,5,6}, P(A) = 1/2, B = {1,2,4,5,8}, P(B) =5/8
Briefly explain the meaning of an estimator and an estimate.
An estimator is a sample statistic used to estimate a population parameter, while an estimate is the value(s) assigned to a population parameter based on the value of a sample statistic.
How do the width and height of a normal distribution change when its mean remains the same but its standard deviation decreases?
As its standard deviation decreases, the width of a normal distribution curve decreases and its height increases
How do the width and height of a normal distribution change when its mean remains the same but its standard deviation increases?
As its standard deviation increases, the width of a normal distribution curve increase and its height decreases
A statistical experiment has eight equally likely outcomes that are denoted by 1,2,3,4,5,6,7, and 8. Let event A={2,5,7} and event B={2,4}. What are the complements of events A and B , and their probabilities?
A¯={1,3,4,6,8} , P(A¯)=5/8, B¯={1,3,5,6,7,8} , P(B¯)=3/4
In order to decide if he should add a kids' menu, a restaurateur counts the number of children at each table in his restaurant. Construct a frequency distribution. 0 2 3 1 4 0 0 1 2 0
Bar graph: 0(4), 1(2), 2(2), 3(1), 4(1)
A July 7, 2011 Pew Research Center poll asked a random sample of Americans to name the current news story that they were following the most at that time. The following table summarizes their responses. Response / Percentage of Responses Casey Anthony verdict 37 Economy 17 Deficit and national debt 14 Last Space Shuttle launch 5 2012 Elections 4 Dominique Strauss-Kahn 1 Other 22 Draw a bar graph to display this percentage distribution. Let the seven categories listed in the table be denoted by CA, EC, D, SS, EL, DSK, and O respectively.
Bar graph: CA(37), EC(17), D(14), SS(5), EL(4), DSK(1), O(22)
40 adults were asked which of the following conveniences they would find most difficult to do without: television (T), refrigerator (R), air conditioning (A), public transportation (P), or microwave (M). Their responses are listed below. PARPPPTRPAAAATRARPATPAARRTTRRRRTAPTRAAAR
Class / Frequency / Relative Frequency / Percentage T 7 0.175 17.5 R 12 0.3 30 A 13 0.325 32.5 P 8 0.2 20 What percentage of surveyed adults named refrigerator or air conditioning as the convenience that they would find most difficult to do without? Enter the exact answer. 62.5%
A July 2011 ESPN SportsNation poll asked, "Which is the best Fourth of July weekend sports tradition?" The choices were Major League baseball game (B), Nathan's Famous International Hot Dog Eating Contest (H), Breakfast at Wimbledon (W), or NASCAR race at Daytona (N). The following data represent the responses of a random sample of 45 persons who were asked the same question. HBNHBBBHBBWBWNHHWBHHWBHWNNHHBWHWNWHBNHHBBNHHW
Frequency distribution table: Category / Frequency B 13 H 16 W 9 N 7 Relative frequencies and percentage: Category / Relative Frequency / Percentage B 0.289 28.9 H 0.356 35.6 W 0.200 20.0 N 0.156 15.6 Relative frequency of a category = frequency of that category/sum of all frequencies What percentage of the respondents mentioned Major League baseball game or NASCAR race at Daytona?Round your answer to one decimal place. About 44.5% of the respondents mentioned Major League baseball game or NASCAR race at Daytona
The following data give the amounts spent (in dollars) on refreshments by 30 spectators randomly selected from those who patronized the concession stands at a recent Major League Baseball game. 4.00 25.00 8.00 5.80 4.00 2.99 4.85 6.00 9.00 15.00 9.00 3.00 5.65 21.00 16.00 18.00 21.77 12.35 7.75 10.00 3.00 28.00 8.35 17.70 19.00 11.65 11.45 3.00 6.55 16.00 Construct a frequency distribution table using the less-than method to write classes. Take $0 as the lower boundary of the first class and $6 as the width of each class. Calculate the relative frequencies and percentages for all classes. Use the data obtained to choose a correct histogram for the frequency distribution.
Histogram: 0-6(9), 6-12(10), 12-18(5), 18-24(4), 24-30(2)
You report a 95% confidence interval for a proportion as 53% ± 4%. Choose the most accurate statement below.
If you did this many times, 95% of those times, the true population proportion would be within your confidence interval.
Correct answer iconYour answer is correct. The following data give the 2015 bonuses (in thousands of dollars) of 15 randomly selected Wall Street managers. 115 116 179 80 62 366 65 248 70 788 144 204 393 244 66 Prepare a box-and-whisker plot.
Left tail(50), 1st line(70), median(150), 3rd line( 250), right tail(400), outlier(800)
Prices of a certain item have a distribution that is skewed to the right with outliers in the right tail. Which of the measures of central tendency is the best to summarize this data set?
Median
You randomly select two households and observe whether or not they own a telephone answering machine. Which of the following is a simple event?
Neither of the two owns a telephone answering machine.
To prove that girls are smarter than boys, Janae compares the SAT scores of the girls in honors classes to the SAT scores of the boys in special education. She reports a 95% confidence interval for the difference of (390, 430). Has she proved that girls will score about 400 higher on the SAT?
No
A data set on money spent on lottery tickets during the past year by 200 households has a lowest value of $1 and a highest value of $1040. Suppose we want to group these data into 6 classes of equal widths. Assuming we take the lower limit of the first class as $1 and the width of each class equal to $200, what are the class boundaries and class midpoints?
Number of Class / Lower Boundary / Upper Boundary / Class Midpoint 1 0.5 200.5 100.5 2 200.5 400.5 300.5 3 400.5 600.5 500.5 4 600.5 800.5 700.5 5 800.5 1000.5 900.5 6 1000.5 1200.5 1100.5
A data set on money spent on lottery tickets during the past year by 200 households has a lowest value of $1 and a highest value of $515. Suppose we want to group these data into 6 classes of equal widths. Assuming we take the lower limit of the first class as $1 and the width of each class equal to $100, write the class limits for all six classes.
Number of Class / Lower Limit / Upper Limit 1 1 100 2 101 200 3 201 300 4 301 400 5 401 500 6 501 600
Find the following probability for the standard normal distribution. Round your answer to four decimal places.
P(0.31≤z≤1.72)= .3356
The probability of the union of two events A and B, that are mutually exclusive, is:
P(A)+P(B).
The probability of the union of two events A and B is:
P(A)+P(B)−P(A and B).
The probability of the intersection of two events A and B is given by:
P(A)P(B|A).
Two events A and B are independent if
P(A|B) is equal to P(A).
In a May 4, 2011 Quinnipiac University poll, a random sample of New York City residents were asked, "How serious is the problem of police officers fixing tickets: very serious, somewhat serious, not too serious, or not at all serious?" (Note: In 2010 to 2011, New York City investigated the widespread problem of traffic ticket fixing by police officers. Many police officers were charged with this crime after the investigation.) The following table summarizes residents' responses. Response / Percentage of Responses Very serious 38 Somewhat serious 26 Not too serious 17 Not at all serious 8 Note that these percentages add up to 89%. The remaining respondents stated that they did not know or had no opinion. Assume that 11% belong to the category did not know. Draw a pie chart for this percentage distribution. Let the four categories listed in the table be denoted by V,S,NTS, and NAS respectively, and let DK/NA represent "did not know or had no opinion."
Pie chart: DK/NA (11%), V (38%), S (26%), NTS (17%), NAS (8%)
In 2007/2008 basketball season, Steve Nash scored 485 field goals, 179 3-point field goals, and 222 free-throw goals. Find the pie chart that better describes the data.
Pie chart: Field goals largest, 3-point goals middle, free throw goals smallest
The following data give the numbers of driving citations received by 12 drivers. 3 0 7 5 7 7 8 1 8 7 7 2 Assume we have found the range, variance and standard deviation. Are the values of these summary measures population parameters or sample statistics?
Sample statistics
The following data give the numbers of driving citations received by 12 drivers. 5 0 9 7 11 9 12 1 13 9 8 3 Assume we have found the range, variance and standard deviation. Are the values of these summary measures population parameters or sample statistics?
Sample statistics
Which of the following is not a binomial experiment?
Selecting 50 adults and observing if they are in favor of an issue, against it, or have no opinion.
One disadvantage of the standard deviation as a measure of dispersion is that it is a measure of absolute variability and not of relative variability. Sometimes we may need to compare the variability of two different data sets that have different units of measurement. The coefficient of variation is one such measure. The coefficient of variation, denoted by CV, expresses standard deviation as a percentage of the mean and is computed as follows: For population data: CV=σ/μ×100% For sample data: CV=s/x¯×100% The yearly salaries of all employees who work for a company have a mean of $64,250 and a standard deviation of $6030. The years of experience for the same employees have a mean of 16 years and a standard deviation of 5 years. Is the relative variation in the salaries larger or smaller than that in years of experience for these employees?
Smaller
The following table gives the state taxes (in dollars) on a pack of cigarettes for nine states as of April 1, 2009. State / State Tax (in dollars) Alaska 2.00 Iowa 1.36 Massachusetts 2.51 Missouri 0.17 New Hampshire 1.33 New York 2.75 Ohio 1.25 South Carolina 0.07 West Virginia 0.55 What is the variable for this data set?
State tax
A financial expert believes that the probability is 0.12 that the stock price of a specific technology company will double over the next year. Is this a case of classical, relative frequency, or subjective probability?
Subjective probability
The president of a company has a hunch that there is a 0.40 probability that the company will be successful in marketing a new brand of ice cream. Is this a case of classical, relative frequency, or subjective probability?
Subjective probability
The president of a company has a hunch that there is a 0.60 probability that the company will be successful in marketing a new brand of ice cream. Is this a case of classical, relative frequency, or subjective probability?
Subjective probability
An economist says that the probability is 0.47 that a randomly selected adult is in favor of keeping the Social Security system as it is, 0.32 that this adult is in favor of totally abolishing the Social Security system, and 0.21 that this adult does not have any opinion or is in favor of other options. Were these probabilities obtained using the classical approach, relative frequency approach, or the subjective probability approach?
Subjective probability approach.
A population has a distribution that is skewed to the left. Indicate whether the central limit theorem will apply to describe the sampling distribution of the sample mean of size n=33.
The central limit theorem can be applied.
A population has a distribution that is skewed to the left. Indicate whether the central limit theorem will apply to describe the sampling distribution of the sample mean of size n=31.
The central limit theorem can be applied.
Indicate whether the central limit theorem will apply to describe the sampling distribution of the sample proportion. n=25 and p=0.30
The central limit theorem can be applied.
Indicate whether the central limit theorem will apply to describe the sampling distribution of the sample proportion. n=33 and p=0.45
The central limit theorem can be applied.
Indicate whether the central limit theorem will apply to describe the sampling distribution of the sample proportion. n=95 and p=0.22
The central limit theorem can be applied.
Indicate whether the central limit theorem will apply to describe the sampling distribution of the sample proportion. n=70 and p=0.05
The central limit theorem cannot be applied.
An independent group wants to determine if the consumption of gasoline has increased due to changes in price. The group randomly selects 320 gas stations from 12 different states and collects data from the month of the year when gas is the cheapest and from the month of the year when gas is the most expensive. The data shows no significant difference in gas consumption between the two months. In this example, what is the variable being studied?
The consumption of gasoline..
A population has a distribution that is skewed to the right. A sample of size n is selected from this population. Describe the shape of the sampling distribution of the sample mean for the following case. n=80
The distribution is approximately normal.
A population has a distribution that is skewed to the right. A sample of size n is selected from this population. Describe the shape of the sampling distribution of the sample mean for the following case. n=22
The distribution is slightly skewed to the right.
Please view the following video before answering this question. Measures of Center Which of the following is true?
The mathematical calculations of the population mean and the sample mean are the same and the symbols are different.
If a data set is right-skewed with one peak in the histogram, then which of the following is true?
The mean is greater than the median, which is greater than the mode.
Which of the following is an example of a discrete random variable?
The number of horses owned by a farmer.
In a survey of 630 parents of young children, 340 said that they will not want their children to play football because it is a very dangerous sport, 220 said that they will let their children play football, and 70 had no opinion. Considering the opinions of these parents, what is the mode?
The opinion that they will not allow their children to play football.
Which of the following is not an acceptable condition for using the t distribution to make a confidence interval for μ?
The population from which the sample is drawn is right-skewed and n < 30.
Let x be a continuous random variable. What is the probability that x assumes a single value, such as a?
The probability is 0.
What is the difference between the probability distribution of a discrete random variable and that of a continuous random variable?Select each correct answer.
The probability that a continuous random variable x assumes a value within a certain interval is given by the area under the curve between the two limits of the interval. For a discrete random variable the value is given by the summation of values between those two points. A discrete random variable has countable values, a continuous random variable has values that are not countable. The probability distribution of a discrete random variable assigns probabilities to points while that of a continuous random variable assigns probabilities to intervals.
Check if the sample size is large enough to use the normal distribution to make a confidence interval for p for the following case. n=892 and p^=0.15
The sample size is large enough
Check if the sample size is large enough to use the normal distribution to make a confidence interval for p for the following case. n=900 and p^=0.15
The sample size is large enough
Check if the sample size is large enough to use the normal distribution to make a confidence interval for p for the following case. n=55 and p^=0.08
The sample size is not large enough
Check if the sample size is large enough to use the normal distribution to make a confidence interval for p for the following case. n=60 and p^=0.08
The sample size is not large enough(np wasn't larger than 5)
A population has a normal distribution. A sample of size n is selected from this population. Describe the shape of the sampling distribution of the sample mean for the following case. n =21
The shape is normal.
A population has a normal distribution. A sample of size n is selected from this population. Describe the shape of the sampling distribution of the sample mean for the following case. n=16
The shape is normal.
A population has a normal distribution. A sample of size n is selected from this population. Describe the shape of the sampling distribution of the sample mean for the following case. n=390
The shape is normal.
A population has a normal distribution. A sample of size n is selected from this population. Describe the shape of the sampling distribution of the sample mean for the following case. n=79
The shape is normal.
Which of the following is not an example of a discrete random variable?
The time spent by a physician with a patient.
Explain the meaning of a point estimate and an interval estimate.
The value of a sample statistic used to estimate a population parameter is called a point estimate. In interval estimation, an interval is constructed around the point estimate, and it is stated that this interval is likely to contain the corresponding population parameter.
Which of the following is not a characteristic of the normal distribution?
The value of the mean is always greater than the value of the standard deviation.
The following data give the number of students suspended for bringing weapons to schools in the Tri-City School District for each of the past 12 weeks. 17 4 16 6 13 7 12 7 11 8 10 10 Determine the values of the three quartiles and the interquartile range. Where does the value of 11 fall in relation to these quartiles?
The values of the three quartiles are 7,10,12.5 and the interquartile range equals 5.5. So, the value 11 falls in the region between 10 and 12.5.
Do the width and/or height of a normal distribution change when its standard deviation remains the same but its mean decreases?
The width of a normal distribution curve remains the same and its height remains the same when its standard deviation remains the same but its mean decreases
Which of the following is not a condition to apply the Poisson probability distribution?
There are n identical occurrences.
Which of the following is not a condition of the binomial experiment?
There are only two trials.
Which of the following is an example of a binomial experiment?
Tossing a coin 20 times and observing for a head or tail.
A survey of 1,000 households gives the probability distribution: Number of cars owned / Probability 1 0.459 2 0.368 3 0.145 4 or more 0.028 Is this a valid probability distribution?
Yes
The normal probability distribution is applied to:
a continuous random variable.
A discrete variable is a variable that can assume:
a countable set of values only.
A distribution curve that is right-skewed has:
a longer tail on the right side
The following table gives the number of dog bites reported to the police last year in six cities. City Number of Bites Center City 38 Elm Grove 46 Franklin 18 Bay City 38 Oakdale 30 Sand Point 24 With reference to this table, what is Franklin ?
a member
When preparing a frequency distribution, the lower limit of the first class should always be:
a number that is less than or equal to the smallest value in the data set
In statistics, we define a sample as:
a portion of the population.
A Bernoulli trial is:
a repetition of a binomial experiment.
According to the U.S. Department of Agriculture, the average American consumed 54.3 pounds (approximately seven gallons) of salad and cooking oils in 2008. Suppose that the current distribution of salad and cooking oil consumption is approximately normally distributed with a mean of 54.3 pounds and a standard deviation of 14.5 pounds. Round your answers to two decimal places. a. What percentage of Americans' annual salad and cooking oil consumption is less than 15 pounds? b. What percentage of Americans' annual salad and cooking oil consumption is between 45 and 65 pounds? c. What percentage of Americans' annual salad and cooking oil consumption is more than 95 pounds? d. What percentage of Americans' annual salad and cooking oil consumption is between 55 and 75 pounds?
a) .34% b) 50.93% c) .25% d) 40.37%
The SCT is a standardized test with a known normal distribution having a mean of 18 and a standard deviation of 3. a) What percentile would a score of 12 be? b) What percentile would a score of 20 be? c) What score corresponds to the 85th percentile?
a) 2nd percentile b) 75th percentile c) Score = 21
The weights of apples from a certain orchard are normally distributed with a mean of 0.8 pounds and a standard deviation of 0.2 pounds. a) What percentage of apples weigh between 0.6 and 1 pound? b) 95% of apples weigh between what two values? c) 16% of apples weigh more than what amount? d) Only 0.15% of apples are as small as or smaller than what weight?
a) 68% b) between 0.4 and 1.2 pounds c) more than 1.0 pound(s) d) 0.2 pounds
The probability distribution table of a discrete random variable lists:
all of the values that the random variable can assume and their corresponding probabilities.
In statistics, a population consists of:
all subjects or objects whose characteristics are being studied.
The mean of the sampling distribution of the sample mean is:
always equal to the population mean.
For a discrete random variable x, the probability of any value of x is:
always in the range zero to 1.
If the population from which samples are drawn is normally distributed, then the sampling distribution of the sample mean is:
always normally distributed.
A sample point is
an element of a sample space.
A marginal probability is a probability of
an event without considering any other event.
A continuous variable is a variable that can assume:
an uncountable set of values.
A continuous random variable x has a left-skewed distribution with a mean of 155 and a standard deviation of 28. The sampling distribution of the sample mean for a sample of 75 elements taken from this population is:
approximately normal.
A continuous random variable x has a right-skewed distribution with a mean of 80 and a standard deviation of 12. The sampling distribution of the sample mean for a sample of 50 elements taken from this population is:
approximately normal.
If the population from which samples are drawn is not normally distributed, then the sampling distribution of the sample mean is:
approximately normally distributed if n is 30 or larger.
A continuous random variable is a random variable that can:
assume any value in one or more intervals.
A quantitative variable is the only type of variable that can:
assume numeric values for which arithmetic operations make sense.
A compound event includes
at least two outcomes.
In a frequency distribution, the classes should always:
be non-overlapping
The probability of an event is always
between 0 and 1, inclusive
A qualitative variable is the only type of variable that:
cannot be measured numerically.
Two mutually exclusive events
cannot occur together.
In statistics, conducting a census means:
collecting information from all members of the population
In statistics, conducting a survey means:
collecting information from elements.
A data set is a:
collection of observations on one or more variables
The intersection of two events A and B is made up of the outcomes that are:
common to both A and B.
Raw data are the data that:
data recorded in the sequence in which they are collected.
As the sample size increases, the standard deviation of the sampling distribution of the sample mean:
decreases.
The quantity x−μ is called the:
deviation of x from the mean.
The procedure for obtaining the relative frequency of a class is to:
divide the frequency of that class by the sum of all frequencies
The procedure for obtaining the midpoint of a class is to:
divide the sum of the two class limits by 2
We obtain the relative frequency of a category by:
dividing the frequency of that category by the sum of all frequencies
Two events are independent if the occurrence of one event
does not affect the probability of the occurrence of the other event.
A random sample is a sample drawn in such a way that:
each member of the population has some chance of being included in the sample.
A simple random sample is a sample drawn in such a way that:
each sample of the same size has an equal chance of being selected.
The probability of the union of two events A and B is the probability that:
either event A or event B or both A and B happen.
The total area under a normal distribution curve to the left of the mean is always:
equal to 0.5.
The total area under a normal distribution curve to the right of the mean is always:
equal to 0.5.
For the probability distribution of a discrete random variable x, the sum of the probabilities of all values of x must be:
equal to 1
For a continuous random variable x, the total area under the probability distribution curve of x is always:
equal to 1.
For a continuous random variable x, the total probability of all (mutually exclusive) intervals within which x can assume a value is:
equal to 1.
For a normal distribution, the z value for the mean is always:
equal to zero.
The probability that a continuous random variable x assumes a single value is always:
equal to zero.
The values assigned to a population parameter based on the value(s) of a sample statistic are:
estimate(s).
The sample statistic used to estimate a population parameter is a(n):
estimator.
The mean of a discrete random variable is its:
expected value.
For most distributions, we can use the normal distribution to make a confidence interval for a population mean provided that the population standard deviation σ is known and the sample size is:
greater than or equal to 30.
In a frequency histogram, the frequency of a class is the:
height of the corresponding bar
For a continuous random variable x, the area under the probability distribution curve between any two points is always:
in the range zero to 1.
For a continuous random variable x, the probability that x assumes a value in an interval is:
in the range zero to 1.
A simple event
includes one and only one outcome.
An event
includes one or more outcomes.
If P(A∩B)=P(A)P(B), then events A and B are
independent.
A symmetric distribution curve:
is identical on both sides of the mean
You can decrease the width of a confidence interval by:
lowering the confidence level or increasing the sample size.
The width of a confidence interval depends on the size of the:
margin of error.
An outlier influences which of the following summary measures the most?
mean.
The scores of eight students taking a mathematics test are 87, 93, 76, 6, 84, 90, 95, and 73. The best measure of central tendency in this case is the:
median
Which of the following is the only measure that can be calculated for qualitative data?
mode.
The procedure for obtaining the percentage for a class is to:
multiply the relative frequency of that class by 100
We obtain the percentage of a category by
multiplying the relative frequency of that category by 100
When making a confidence interval for the population mean using the t procedures, the degrees of freedom for the t distribution are:
n - 1.
The parameters of the binomial probability distribution are:
n and p.
According to the Central Limit Theorem, the sampling distribution of the sample mean is approximately normal, irrespective of the shape of the population distribution, if:
n is 30 or larger.
To apply the Central Limit Theorem to the sampling distribution of the sample mean, the required sample is typically large enough if:
n is 30 or larger.
For a normal distribution, the z value for an x value that is to the left of the mean is always:
negative.
The tails of a normal distribution curve:
never meet or cross the horizontal axis.
An error that occurs because of human mistakes is called:
nonsampling error.
A continuous random variable x has a normal distribution with a mean of 90 and a standard deviation of 15. The sampling distribution of the sample mean for a sample of 16 elements taken from this population is:
normal.
In the case of proportion, the sample size is large if:
np and nq are both greater than 5.
We can use the normal distribution to approximate the binomial distribution when:
np and nq are both more than 5.
The mean of a binomial distribution is equal to:
np.
Cross-section data are collected:
on different elements at the same point in time.
Time-series data are collected:
on the same element for the same variable at different points in time.
A random variable is a variable whose value is determined by the:
outcome of a random experiment.
The binomial probability distribution is symmetric if:
p is equal to 0.50.
The binomial probability distribution is left-skewed if:
p is greater than 0.50.
The binomial probability distribution is right-skewed if:
p is less than 0.50.
The single value of a sample statistic that we assign to the population parameter is a:
point estimate.
The population distribution is the probability distribution of the:
population data.
Estimation is a procedure by which we assign a numerical value or numerical values to the:
population parameter based on the information collected from a sample.
For a normal distribution, the z value for an x value that is to the right of the mean is always:
positive.
The mean of a discrete random variable is the mean of its:
probability distribution.
The standard deviation of a discrete random variable is the standard deviation of its:
probability distribution.
If you divide the number of elements in a population with a specific characteristic by the total number of elements in the population, the dividend is the population:
proportion.
The mean of the sampling distribution of the sample proportion is equal to the population:
proportion.
