93 terms

# Statistical Analysis

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To conduct a survey about the type of phone service most people in Greenville prefer, 10 different blocks in the neighborhood are chosen. On these 10 blocks, 10 houses are selected at random, and then one resident of each of those houses is interviewed. This type of sampling method is
cluster sampling.
A researcher wants to survey people from different age groups to analyze voting patterns. Which type of survey will best accomplish this goal?
stratified sampling
A high school student volunteers to present a report to the administration about the types of lunches students prefer. He surveys members of his class and records their choices. What type of sampling did the student use?
convenience sampling
Which survey is most likely affected by bias?
a survey of students about vacation policies in a school district
Voluntary sampling is one type of sampling method that is not probability based. This means that
the results of the survey cannot reliably be extended and generalized.
Researchers compare the body composition of cattle feeding on a grain diet with that of cattle feeding on a grass diet. This method of gathering data is classified as
Not a sample survey.
A random number generator is used to model the patterns of animals in the wild. This type of study is called
a simulation.
Researchers periodically survey a few thousand of the patients taking a certain medication in order to make connections between that medication and the subjects' general health. This method of gathering data is classified as
an observational study.
The president of the math club is conducting a survey to see where the twelfth-grade class wants to go on their field trip. Instead of asking the whole class, she surveys only the twelfth-grade members of the math club. She records their choices and plans to present the results to the school principal. What type of sampling did she use?
convenience sampling
Brand Y Cola sponsors a survey of 15,559 residents of Texas to determine which brand of cola they prefer. Forty percent say they prefer Brand X, and 60 percent say they prefer Brand Y. Which of the following is the population sample?
the 15,559 residents
The population of a town is divided into three age categories. A random sample of each category is surveyed about voting choices. This type of sampling is called
stratified sampling.
Researchers are conducting a survey about what brand of ice cream shoppers prefer. They survey the tenth person who walks into the store and then every fifth person after that. This type of sampling is called
systematic random sampling.
A teacher asks students to list the math lessons they learned on nine random school days in the past month. She evaluates the students' performance on this assignment to get a general picture of how well students are taking notes. This teacher's method is an example of
simple random sampling.
A company wants to learn about the number of its employees who visit the dentist for regular checkups. Which type of study will best help the company discover this information?
census
The histograms below show the ages of dogs at four different shelters. For which set of data is the mean most likely greater than the median?
Not d
The stem-and-leaf plot below shows the amount of tips received by the servers in a restaurant in one night.
mc017-1.jpg
Why is the plot misleading?
Not There is not an equal number of data points for each stem. or The plot shows that the data is skewed.
Charles owns a catering business. The amount his 10 most recent clients spent is shown in the histogram below.

mc018-1.jpg

Why is the graph misleading?
Not The scales are different on the x-axis and the y-axis.
The graph below is used by company 2 to show the average monthly electric cost based on the electricity provider.

mc023-1.jpg

How could the graph be redrawn so that the difference in monthly electric cost does not appear as great?
Not The interval on the y-axis could be changed to count by 20s. or The scale on the y-axis could be changed to 100-120.
The box plots below show the ages of college students in different math courses.

mc003-1.jpg mc003-2.jpg
Math 1 Math 2

Which statement is true?
The mean and median age are more likely to be the same for the students in Math 1.
A histogram shows data that is skewed to the right. Which most likely describes the relationship between the mean and the median?
The mean is greater than the median. The rightmost values in the data set raise the mean more than the median.
A representative from plan 1 wants to use the graph below to sell health plans for his company.

mc020-1.jpg

How might the graph be redrawn to emphasize the difference between the cost per doctor visit for each of the three plans?
Not The scale on the y-axis could be changed to 0-100.
A poll asks shoppers at the mall how many cups of water they typically drink in a day. The results of the poll are listed below.

3, 5, 5, 6, 6, 6, 7, 7, 8, 8, 8, 8, 8, 8, 9, 9, 10, 10, 10, 10, 11

What is value of the first quartile?
Not 8
The histogram below shows the estimated monthly salaries of company employees with different years of experience.

mc014-1.jpg

How might the graph be misleading?
Not The scale on the x-axis underemphasizes the difference in salaries between different experience levels.
Thirty adults were asked how many pets they have had over their lifetime. The results are shown in the histogram below.

mc007-1.jpg

Which of the following is most likely true?
Not The mean is in the interval 6-10, and the median is in the interval 1-5.
The histogram below shows the age distribution of Elizabeth's grandchildren.

mc024-1.jpg

The box-and-whisker plot below shows the same data.

mc024-2.jpg

Which of the following best explains why one graph appears skewed and one graph appears symmetric?
The interval on the x-axis of the histogram is inconsistent.
The histogram below shows the number of weeks Jimmy spent different amounts of money to fill the gas tank in his car.

mc021-1.jpg

If the graph is redrawn so that the scale on the y-axis begins with zero, which aspect of the graph will change the most?
Not The graph will appear more skewed to the right.
The box-and-whisker plot below shows the age distribution of people at a family reunion.

mc022-1.jpg

The stem-and-leaf plot below shows the same data.

mc022-2.jpg

Which of the following best explains why one graph appears skewed and one graph appears symmetrical?
Not The interval of the box-and-whisker plot is too large.
Thirty adults were asked how many pets they have had over their lifetime. The results are shown in the histogram below.

mc007-1.jpg

Which of the following is most likely true?
Not The mean and median are both in the interval 1-5.
The stem-and-leaf plot below shows the number of pages each student in a class read the previous evening.

mc011-1.jpg

Which statement is true about the data set?
Not The data is symmetric.
Indira makes a box-and-whisker plot of her data. She finds that the distance from the minimum value to the first quartile is greater than the distance between the third quartile and the maximum value. Which is most likely true?
Not The mean is greater than the median because the data is skewed to the left.
The hourly wages earned by 20 employees are shown in the first box-and-whisker plot below. The person earning \$15 per hour quits and is replaced with a person earning \$8 per hour. The graph of the resulting salaries is shown in plot 2.

mc013-1.jpg
Plot 1

mc013-2.jpg
Plot 2

How does the mean and median change from plot 1 to plot 2?
Not The mean and median decrease.
The mean test scores with standard deviations of four English classes are given below.

Class
Mean
Standard Deviation
Mrs. Jones
89
1.9
Mrs. Rijo
82
1.4
Mr. Phan
73
3.4
Mrs. Scott
90
6.1

Which statement is most likely to be true?
The scores of Mrs. Rijo's class are the closest to the class mean.
Opal is collecting data on water levels in different parts of town. She notices that her sample data has a low-value outlier. Which statement must be true?
Removing the outlier will decrease the spread of the graph of the data set.
A supervisor finds the mean number of miles that the employees in a department live from work. He finds mc022-1.jpg and mc022-2.jpg. Which statement must be true?
z37 is between 2 and 3 standard deviations of the mean.
Emi computes the mean and variance for the population data set 87, 46, 90, 78, and 89. She finds the mean is 78. Her steps for finding the variance are shown below.

mc008-1.jpg

What is the first error she made in computing the variance?
Emi evaluated (46 - 78)2 as -(32)2.
The mean of a set of credit scores is mc021-1.jpg and mc021-2.jpg. Which credit score is within a z-score of 3.3?
720
Which formula is used to calculate the standard deviation of sample data?
A mc001-1.jpg
Yuri computes the mean and standard deviation for the sample data set 12, 14, 9, and 21. He finds the mean is 14. His steps for finding the standard deviation are below.

mc007-1.jpg

What is the first error he made in computing the standard deviation?
Yuri divided by n instead of n -1.
A scientist collected two sample sets of snowfall data. Which statistic should he use to compare the spread of the two sets of data?
standard deviation
A set of data has a mean of 12 and a standard deviation of 3. A data point of the set has a z-score of 1.3. What does a z-score of 1.3 mean?
The data point is 1.3 standard deviations away from 12.
A poll worker analyzing the ages of voters found that mc024-1.jpg and mc024-2.jpg. What is a possible voter age that would give her zx = 1.14? Round your answer to the nearest whole number.
Not 66
The lengths of a lawn mower part are approximately normally distributed with a given mean mc021-1.jpg = 4 in. and standard deviation mc021-2.jpg = 0.2 in. What percentage of the parts will have lengths between 3.8 in. and 4.2 in.?
Not 34% or 95%
The graph below shows three different normal distributions.
mc008-1.jpg

Which statement must be true?
Each distribution has a different mean and a different standard deviation.
The heights of a certain type of tree are approximately normally distributed with a mean height mc018-1.jpg = 5 ft and a standard deviation mc018-2.jpg = 0.4 ft. Which statement must be true?
Not A tree with a height of 5.4 ft is 1 standard deviation below the mean. or A tree with a height of 4.6 ft is 1 standard deviation above the mean.
The graph below shows the average daily temperatures on January 1 from 1900 to 1934 for city A.

mc006-1.jpg

The mean of the temperatures in the chart is 24° with a standard deviation of 4°. Which temperature is within one standard deviation of the mean?
27°
The set of life spans of an appliance is normally distributed with a mean mc013-1.jpg = 48 months and a standard deviation mc013-2.jpg = 8 months. What is the life span of an appliance that has a z-score of -3?
24 months
The grades of a science test are normally distributed. Thanh finds that his grade on the test has a z-score of -2.5. Which statement must be true?
Not Thanh's grade is 2.5 points below the mean of the test grades.
The set of life spans of an appliance is normally distributed with a mean mc012-1.jpg = 48 months and a standard deviation mc012-2.jpg = 8 months. What is the z-score of an appliance that stopped working at 64 months?
2
The average miles per gallon of a particular automobile model are approximately normally distributed with a given mean mc024-1.jpg = 43.8 miles per gallon and standard deviation mc024-2.jpg = 5.1 miles per gallon. What percentage of the automobiles have an average miles per gallon between 38.7 miles per gallon and 48.9 miles per gallon?
68%
The scores of a high school entrance exam are approximately normally distributed with a given mean mc023-1.jpg = 82.4 and standard deviation mc023-2.jpg = 3.3. What percentage of the scores are between 75.8 and 89?
95%
Which normal distribution has the greatest standard deviation?
c
The amount of daily time that teenagers spend on a brand A cell phone is normally distributed with a given mean mc027-1.jpg = 2.5 hr and standard deviation mc027-2.jpg = 0.6 hr. What percentage of the teenagers spend more than 3.1 hr?
16%
The graph below shows the average daily temperatures on January 1 from 1900 to 1934 for city A.

mc007-1.jpg

The mean of the temperatures in the chart is 24° with standard deviation of 4°. How many years had temperatures within one standard deviation of the mean?
25
The scores of an eighth-grade math test have a normal distribution with a mean mc011-1.jpg = 83 and a standard deviation mc011-2.jpg = 5. If Din's test score was 92, which expression would she write to find the z-score of her test score?
c
The graph below shows the average daily temperatures on January 1 from 1900 to 1934 for city A.

mc005-1.jpg

The mean of the temperatures in the chart is 24° with a standard deviation of 4°. Which temperature is within one standard deviation of the mean?
22
The lengths of a particular snake are approximately normally distributed with a given mean mc025-1.jpg = 15 in. and standard deviation mc025-2.jpg = 0.8 in. What percentage of the snakes are longer than 16.6 in.?
Not 3.5%
The lengths of a certain species of fish are approximately normally distributed with a given mean mc019-1.jpg and standard deviation mc019-2.jpg. According to the Empirical Rule, what percentage of the fish will have lengths within 1 standard deviation of the mean?
Not 47.5%
The weights of 2-pound bags of Best Dog Food are approximately normally distributed with a given mean mc020-1.jpg and standard deviation mc020-2.jpg. According to the Empirical Rule, what percentage of the bags will have lengths within 3 standard deviations of the mean?
99.7%
What is the mean of the normal distribution shown below?

mc001-1.jpg
0
The weights of boxes of candies produced in a factory are normally distributed with a mean weight of 16 oz and a standard deviation of 1 oz. What is the weight of a box of candies with a z-score of 2?
Not 20 oz
The times taken to assemble a clock at a factory are approximately normally distributed with a given mean mc022-1.jpg = 3 hr and standard deviation mc022-2.jpg = 0.5 hr. What percentage of the times are between 2 hr and 4 hr?
Not 68%
For a standard normal distribution, which of the following expressions must always be equal to 1?
Not B or A
What is the approximate area of the shaded region under the standard normal curve below? Use the portion of the standard normal table to help answer the question.

mc009-1.jpg

z
Probability
0.00
0.5000
1.00
0.8413
2.00
0.9772
3.00
0.9987
0.81
What is the approximate area of the shaded region under the standard normal curve below? Use the portion of the standard normal table given to help answer the question.
mc012-1.jpg

z
Probability
0.00
0.5000
1.00
0.8413
2.00
0.9772
3.00
0.9987
0.14
What is the approximate area of the unshaded region under the standard normal curve below? Use the portion of the standard normal table given to help answer the question.

mc016-1.jpg

z
Probability
0.00
0.5000
1.00
0.8413
2.00
0.9772
3.00
0.9987
0.18
What is the approximate area of the unshaded region under the standard normal curve below? Use the portion of the standard normal table given to help answer the question.

mc020-1.jpg

z
Probability
0.00
0.5000
1.00
0.8413
2.00
0.9772
3.00
0.9987
Not 0.16
Dwayne and Alisha both correctly graphed a standard normal curve. Which of the following statements is true?
Both the means and the standard deviations of Dwayne's and Alisha's graphs must be the same.
For a standard normal distribution, which of the following variables always equals 0?
A
For a standard normal distribution, which of the following variables always equals 1?
B
A normal distribution of data has a mean of 15 and a standard deviation of 4. How many standard deviations from the mean is 25?
2.5
A city's annual rainfall totals are normally distributed, and the probability that the city gets more than 43.2 inches of rain in a year is given by mc017-1.jpg. If the standard deviation of the city's yearly rainfall totals is 1.8 inches, what is the city's mean annual rainfall?
Not 41.4 inches
What is the approximate area of the shaded region under the standard normal curve below? Use the portion of the standard normal table to help answer the question.

mc009-1.jpg

z
Probability
0.00
0.5000
1.00
0.8413
2.00
0.9772
3.00
0.9987
0.81
What is the approximate area of the unshaded region under the standard normal curve below? Use the portion of the standard normal table given to help answer the question.

mc016-1.jpg

z
Probability
0.00
0.5000
1.00
0.8413
2.00
0.9772
3.00
0.9987
0.18
About what percentage of the data lies within 2 standard deviations of the mean in a normal distribution?
95%
The probability that a random variable is greater than or equal to z standard deviations from the mean in a standard normal distribution is p%. What can be said with certainty about the probability that the random variable is less than or equal to -z standard deviations from the mean?
Not The probability is greater than p%.
Which of the following probabilities is equal to approximately 0.2957? Use the portion of the standard normal table below to help answer the question.

z
Probability
0.00
0.5000
0.25
0.5987
0.50
0.6915
0.75
0.7734
1.00
0.8413
1.25
0.8944
1.50
0.9332
1.75
0.9599
C
The heights of the trees in a forest are normally distributed, with a mean of 25 meters and a standard deviation of 6 meters. What is the probability that a randomly selected tree in the forest has a height greater than or equal to 37 meters? Use the portion of the standard normal table given to help answer the question.

z
Probability
0.00
0.5000
0.50
0.6915
1.00
0.8413
2.00
0.9772
Not 0.13%
For a standard normal distribution, find the approximate value of mc005-1.jpg. Use the portion of the standard normal table below to help answer the question.

z
Probability
0.00
0.5000
0.22
0.5871
0.32
0.6255
0.42
0.6628
0.44
0.6700
0.64
0.7389
0.84
0.7995
1.00
0.8413
Not 84%
The annual salaries of all employees at a financial company are normally distributed with a mean of \$34,000 and a standard deviation of \$4,000. What is the z-score of a company employee who makes an annual salary of \$54,000?
5
A professor surveys his students about their opinions on how well he taught the course. He puts this survey on the last page of his final exam. Which type of bias will most likely have the strongest effect on the survey results?
response bias
What is the mean of the normal distribution shown below?

mc002-1.jpg
4
The proportions of multiple samples of registered voters who vote are normally distributed, with a mean proportion of 0.38 and a standard deviation of 0.0485. What is the probability that a sample chosen at random has a proportion of registered voters who vote between 0.37 and 0.39? Use the portion of the standard normal table below to help answer the question.

z
Probability
0.00
0.5000
0.04
0.5160
0.21
0.5832
0.37
0.6443
0.38
0.6481
0.39
0.6517
1.00
0.8413
17%
A missing data value from a set of data has a z-score of -2.1. Fred already calculated the mean and standard deviation to be mc025-1.jpg and mc025-2.jpg. What was the missing data value? Round the answer to the nearest whole number.
39
News cameras take an overhead picture of a part of a crowd at an outdoor event. Journalists then count the number of people in the picture and use the sample to estimate the total number of people in the crowd. This process is an example of
cluster sampling.
The times of all 15 year olds who run a certain race are approximately normally distributed with a given mean mc026-1.jpg = 18 sec and standard deviation mc026-2.jpg = 1.2 sec. What percentage of the runners have times less than 14.4 sec?
0.15%
The graph below shows the amount of time Misha spent outside over a 30-day period.

mc016-1.jpg

How might the graph be considered misleading?
The y-interval shows exponential increase rather than linear increase.
The times of the runners in a marathon are normally distributed, with a mean of 3 hours and 50 minutes and a standard deviation of 30 minutes. What is the probability that a randomly selected runner has a time less than or equal to 3 hours and 20 minutes? Use the portion of the standard normal table below to help answer the question.

z
Probability
0.00
0.5000
0.50
0.6915
1.00
0.8413
2.00
0.9772
3.00
0.9987
16%
For a standard normal distribution, if mc007-1.jpg, what is the value of mc007-2.jpg?
0.2884
The histogram below represents the number of points Mandy scored per game. The graph makes the data appear symmetric when it is actually skewed.

mc025-1.jpg

How can the graph be adjusted to show the skew?
The intervals on the x-axis can be changed to be continuous and consistent.
Which measure is most appropriate to describe the center of the data in the stem-and-leaf plot below?

mc002-1.jpg
median
Fiona recorded the number of miles she biked each day last week as shown below.

4, 7, 4, 10, 5

The mean is given by m = 6. Which equation shows the variance for the number of miles Fiona biked last week?
d mc002-4.jpg
The monthly mean salaries and standard deviations of four college students are given below.

Student
Mean
Standard Deviation
Clarissa
\$345
12.53
Abi
\$598
8.99
Kaila
\$812
15.29
Shenika
\$208
7.67

Which statement must be true?
The monthly salary of Shenika is less spread out than the monthly salary of Clarissa.
Which of the following could be classified as a census?
a survey of each student in a school about school lunch options