Statistics All Topics –
Complete Study Guide,
Exam Review, Practice
Questions & Answers
Updated Questions and Answers
100% Verified Exam Prep and Comprehensive
Rationales
Included
,The distribution of the scores on a certain exam is N(40,10 A. se picture
), which means that the exam scores are Normally
distributed with a mean of 40 and standard deviation of 10. B. Using the Empirical Rule, the probability that a randomly selected score will be
lessless than 30 is about 16%.
a. Sketch the curve and label, on the x-axis, the position of
the mean, the mean plus or minus one standard deviation,
the mean plus or minus two standard deviations, and the
mean plus or minus three standard deviations.
b. Find the probability that a randomly selected score will
be lessless than 30. Shade the region under the Normal
curve whose area corresponds to this probability.
A biologist is studying the effects that applying insecticide Having an "unbiased" estimator means that the mean of the means of all possible
to a fruit farm has on the local bat population. She collects samples of the same size would be the same as the population mean.
23 bats and finds the mean weight of this sample to be
503.4 grams. Assuming the selected bats are a random
sample, she concludes that because the sample mean is
an unbiased estimator of the population mean, the mean
weight of bats in the population is also 503.4 grams.
Explain why this is an incorrect interpretation of an
unbiased estimator.
The weight of a group of women has a population mean, a. The expected mean weight is about 127127 pounds, because the sample mean
muμ, of 127 pounds and a population standard deviation, is an unbiased estimator of the population mean.
sigmaσ, of 20 pounds. The distribution is right-skewed.
Suppose a random sample is taken of 100 of these b. The standard error of the sample mean is 2 pounds.
women's weights. (20/sqrt 100).
a. What value should we expect for the mean weight of this
sample of 100 women? Why?
b. The actual sample mean will not be exactly the value
determined in part a. The amount it typically differs from
this value is given by the standard error. What is the
standard error for a sample mean taken from this
population?
One histogram shows the distribution of the length of a The distribution of the length of this person's cell phone calls for the month is shown
certain person's cell phone calls for one month, and the in Histogram B, because this distribution has a
other shows many sample means, in which each is the larger standard deviation, and is
mean length for 2020 randomly selected calls from the skewed in one direction.
same person during that month. Which is which? Explain. The distribution of many sample means for randomly selected calls from the same
person during the month is shown in Histogram
Which is which? Explain. A, because this distribution has a
smaller standard deviation, and is approximately Normal.
,The mean age of all 606 used cars for sale in a newspaper a. From the problem statement, the mean age of all 606 cars in the newspaper is
one Saturday last month was 7.1 years, with a standard 7.1 years.
deviation of 6.8 years. The distribution of ages is right- The value 7.1 years is a characteristic of the population.
skewed. For a study to determine the reliability of classified Therefore, 7.1 is a population parameter.
ads, a reporter randomly selects 6060 of these used cars
and plans to visit each owner to inspect the cars. He finds From the problem statement, the standard deviation of all 606 cars in the
that the mean age of the 6060 cars he samples is 7.6 newspaper is 6.8 years.
years and the standard deviation of those 60 cars is 4.9 The value 6.8 years is a characteristic of the population.
years. Therefore, 6.8 is a population parameter.
a. From the problem statement, which of the values 7.1, From the problem statement, the mean age of the 60 cars the reporter randomly
6.8, 7.6, and 4.9 are parameters and which are statistics? selected is 7.6 years.
The value 7.6 years is a characteristic of the sample.
Recall that a parameter is a numerical value that Therefore, 7.6 is a sample statistic.
characterizes some aspect of the population, and a
statistic is a numerical characteristic of a sample of data From the problem statement, the standard deviation age of the 60 cars the reporter
taken from the population. In this case, the population is all randomly selected is 4.9 years.
606 used cars that were for sale in the newspaper, and the The value 4.9 years is a characteristic of the sample.
sample of data is the 60 cars the reporter randomly Therefore, 4.9 is a sample statistic.
selected for his study.
From the problem statement, the mean age of all 606 cars
in the newspaper is 7.1 years. b. Recall that in this case, the population is all 606 used cars that were for sale in
the newspaper, and the sample of data is the 60 cars the reporter randomly
b. Find μ, σ, s, and overboard. selected for his study.
The population mean μ is 7.1.
c. Are the conditions for using the CLT (Central Limit The population standard deviation σ is 6.8.
Theorem) fulfilled? The sample standard deviation s is 4.9.
The sample mean overbarx is 7.6.
d. What would be the shape of the approximate sampling
distribution of a large number of means, each from a c. First check the random sample/independence condition. The requirements to
sample of 60 cars? fulfill the random sample/independence condition are that each observation is
collected randomly from the population, and observations are independent of each
other.
It is given in the problem statement that the reporter randomly selects 60 used cars
from the population of 606 used cars in the newspaper.
Since finding the age of any one car does not give any information about the ages
of the other cars in the sample, it is safe to assume that the observations are
independent of each other.
Now check the Normal condition. The Normal condition is fulfilled if either the
population distribution is Normal or the sample size is large. It is given that the
population distribution is right-skewed, so check the sample size. For most
applications, a sample size of 25 is large enough. Find the sample size and
compare it to 25.
60≥25. What would be the shape of the approximate sampling distribution of a large
number of means, each from a sample of 60 cars?
---Yes, all the conditions for using the CLT are fulfilled.
d. The CLT states that no matter what the shape of the population distribution, if a
sample is selected such that the relevant conditions are met, then the distribution of
sample means follows an approximately Normal distribution.
--Normal
A random sample of 40 students taking statistics at a a. We are 95% confident that the population mean GPA of statistics students at the
community college was asked their GPA. The sample school is between 3.14 (3.36-0.22) and 3.58 (3.36+0.22).
mean was 3.36, and the margin of error for a 95%
confidence interval was 0.22. b. It tells us a range of plausible values for the population mean GPA, where the
population is all statistics students at the school. Yes, reject 3.94, because it is not
a. Choose the correct interpretation of the confidence in the interval. We are confident that the statistics students have a lowerlower
interval below and fill in the answer boxes to complete your population mean than 3.94.
choice. Assume that the conditions for constructing a
confidence interval are met.
b. What does the interval tell us about the population mean
GPA for statistics students at the school? Can you reject
3.94 as the mean for statistics students? Explain.
, A statistics instructor randomly selected four bags of a. We are 95% confident the population mean is between 9.256 and 9.944.
oranges, each bag labeled 10 pounds, and weighed the
bags. They weighed 9.6, 9.8, 9.3, and 9.7 pounds. Assume b. No, it does not capture 10. Reject the claim of 10 pounds because 10 is not in the
that the distribution of weights is Normal. Find a 95% interval.
confidence interval for the mean weight of all bags of
oranges. Use technology for your calculations.
a. Choose the correct interpretation of the confidence
interval below and, if necessary, fill in the answer boxes to
complete your choice.
b. Does the interval capture 10 pounds? Is there enough
evidence to reject the null hypothesis that the population
mean weight is 10 pounds? Explain your answer.
A random sample of 21 independent female college-aged Use http://www.sample-size.net/confidence-interval-mean/
dancers showed a sample mean height of 64.8 inches and
a sample standard deviation of 1.7 inches. Assume that a. We are 95% confident that the population mean height of female college-aged
this distribution of heights is Normal. dancers is between 64.0 and 65.6
a. Use technology to find a 95% confidence interval for the b. We are 99% confident that the population mean height of female college-aged
population mean height of dancers and interpret the dancers is between 63.7 and 65.9.
interval.
c. The 99% interval is wider because it has a greater confidence level, and therefore
b. Use technology to find a 99% confidence interval for the we use a bigger value of t*, which creates a wider interval
population mean height and interpret the interval.
c. Which interval is wider and why?
State whether each of the following changes would make a a. The interval will become wider.
confidence interval wider or narrower. (Assume that
nothing else changes.) b. The interval will become wider.
a. Changing from a 95% confidence level to a 99% c. The interval will become narrower.
confidence level.
b. Changing from a sample size of 300 to a sample size of
25.
c. Changing from a standard deviation of 25 pounds to a
standard deviation of 15 pounds.
Thirty GPAs from a randomly selected sample of statistics click the table icon, then the window icon, then command c. paste to:
students at a college are linked below. Assume that the http://www.calculatorsoup.com/calculators/statistics/mean-median-mode.php
population distribution is approximately Normal. The
technician in charge of records claimed that the population a. The sample mean is 3.10. It is higher than the population mean of 2.86.
mean GPA for the whole college is 2.86.
b. H0: μ=2.86
a. What is the sample mean? Is it higher or lower than the Ha: μ>2.86
population mean of 2.86?
(to find the test statistic and p-value, open in stat crunch[press table icon, window
b. The chair of the mathematics department claims that icon, open in stat chrunch], then compete a "One sample T hypothesis test" [stat, t-
statistics students typically have higher GPAs than the stat, one sample with data, compute])
typical college student. Use the four-step procedure and
the data provided to test this claim. Use a significance t=3.90
level of 0.05. Which of the following correctly states H0 p=0.000
and Ha?
Reject H0. The mean GPA for statistics students is significantly higher than 2.86.
Complete Study Guide,
Exam Review, Practice
Questions & Answers
Updated Questions and Answers
100% Verified Exam Prep and Comprehensive
Rationales
Included
,The distribution of the scores on a certain exam is N(40,10 A. se picture
), which means that the exam scores are Normally
distributed with a mean of 40 and standard deviation of 10. B. Using the Empirical Rule, the probability that a randomly selected score will be
lessless than 30 is about 16%.
a. Sketch the curve and label, on the x-axis, the position of
the mean, the mean plus or minus one standard deviation,
the mean plus or minus two standard deviations, and the
mean plus or minus three standard deviations.
b. Find the probability that a randomly selected score will
be lessless than 30. Shade the region under the Normal
curve whose area corresponds to this probability.
A biologist is studying the effects that applying insecticide Having an "unbiased" estimator means that the mean of the means of all possible
to a fruit farm has on the local bat population. She collects samples of the same size would be the same as the population mean.
23 bats and finds the mean weight of this sample to be
503.4 grams. Assuming the selected bats are a random
sample, she concludes that because the sample mean is
an unbiased estimator of the population mean, the mean
weight of bats in the population is also 503.4 grams.
Explain why this is an incorrect interpretation of an
unbiased estimator.
The weight of a group of women has a population mean, a. The expected mean weight is about 127127 pounds, because the sample mean
muμ, of 127 pounds and a population standard deviation, is an unbiased estimator of the population mean.
sigmaσ, of 20 pounds. The distribution is right-skewed.
Suppose a random sample is taken of 100 of these b. The standard error of the sample mean is 2 pounds.
women's weights. (20/sqrt 100).
a. What value should we expect for the mean weight of this
sample of 100 women? Why?
b. The actual sample mean will not be exactly the value
determined in part a. The amount it typically differs from
this value is given by the standard error. What is the
standard error for a sample mean taken from this
population?
One histogram shows the distribution of the length of a The distribution of the length of this person's cell phone calls for the month is shown
certain person's cell phone calls for one month, and the in Histogram B, because this distribution has a
other shows many sample means, in which each is the larger standard deviation, and is
mean length for 2020 randomly selected calls from the skewed in one direction.
same person during that month. Which is which? Explain. The distribution of many sample means for randomly selected calls from the same
person during the month is shown in Histogram
Which is which? Explain. A, because this distribution has a
smaller standard deviation, and is approximately Normal.
,The mean age of all 606 used cars for sale in a newspaper a. From the problem statement, the mean age of all 606 cars in the newspaper is
one Saturday last month was 7.1 years, with a standard 7.1 years.
deviation of 6.8 years. The distribution of ages is right- The value 7.1 years is a characteristic of the population.
skewed. For a study to determine the reliability of classified Therefore, 7.1 is a population parameter.
ads, a reporter randomly selects 6060 of these used cars
and plans to visit each owner to inspect the cars. He finds From the problem statement, the standard deviation of all 606 cars in the
that the mean age of the 6060 cars he samples is 7.6 newspaper is 6.8 years.
years and the standard deviation of those 60 cars is 4.9 The value 6.8 years is a characteristic of the population.
years. Therefore, 6.8 is a population parameter.
a. From the problem statement, which of the values 7.1, From the problem statement, the mean age of the 60 cars the reporter randomly
6.8, 7.6, and 4.9 are parameters and which are statistics? selected is 7.6 years.
The value 7.6 years is a characteristic of the sample.
Recall that a parameter is a numerical value that Therefore, 7.6 is a sample statistic.
characterizes some aspect of the population, and a
statistic is a numerical characteristic of a sample of data From the problem statement, the standard deviation age of the 60 cars the reporter
taken from the population. In this case, the population is all randomly selected is 4.9 years.
606 used cars that were for sale in the newspaper, and the The value 4.9 years is a characteristic of the sample.
sample of data is the 60 cars the reporter randomly Therefore, 4.9 is a sample statistic.
selected for his study.
From the problem statement, the mean age of all 606 cars
in the newspaper is 7.1 years. b. Recall that in this case, the population is all 606 used cars that were for sale in
the newspaper, and the sample of data is the 60 cars the reporter randomly
b. Find μ, σ, s, and overboard. selected for his study.
The population mean μ is 7.1.
c. Are the conditions for using the CLT (Central Limit The population standard deviation σ is 6.8.
Theorem) fulfilled? The sample standard deviation s is 4.9.
The sample mean overbarx is 7.6.
d. What would be the shape of the approximate sampling
distribution of a large number of means, each from a c. First check the random sample/independence condition. The requirements to
sample of 60 cars? fulfill the random sample/independence condition are that each observation is
collected randomly from the population, and observations are independent of each
other.
It is given in the problem statement that the reporter randomly selects 60 used cars
from the population of 606 used cars in the newspaper.
Since finding the age of any one car does not give any information about the ages
of the other cars in the sample, it is safe to assume that the observations are
independent of each other.
Now check the Normal condition. The Normal condition is fulfilled if either the
population distribution is Normal or the sample size is large. It is given that the
population distribution is right-skewed, so check the sample size. For most
applications, a sample size of 25 is large enough. Find the sample size and
compare it to 25.
60≥25. What would be the shape of the approximate sampling distribution of a large
number of means, each from a sample of 60 cars?
---Yes, all the conditions for using the CLT are fulfilled.
d. The CLT states that no matter what the shape of the population distribution, if a
sample is selected such that the relevant conditions are met, then the distribution of
sample means follows an approximately Normal distribution.
--Normal
A random sample of 40 students taking statistics at a a. We are 95% confident that the population mean GPA of statistics students at the
community college was asked their GPA. The sample school is between 3.14 (3.36-0.22) and 3.58 (3.36+0.22).
mean was 3.36, and the margin of error for a 95%
confidence interval was 0.22. b. It tells us a range of plausible values for the population mean GPA, where the
population is all statistics students at the school. Yes, reject 3.94, because it is not
a. Choose the correct interpretation of the confidence in the interval. We are confident that the statistics students have a lowerlower
interval below and fill in the answer boxes to complete your population mean than 3.94.
choice. Assume that the conditions for constructing a
confidence interval are met.
b. What does the interval tell us about the population mean
GPA for statistics students at the school? Can you reject
3.94 as the mean for statistics students? Explain.
, A statistics instructor randomly selected four bags of a. We are 95% confident the population mean is between 9.256 and 9.944.
oranges, each bag labeled 10 pounds, and weighed the
bags. They weighed 9.6, 9.8, 9.3, and 9.7 pounds. Assume b. No, it does not capture 10. Reject the claim of 10 pounds because 10 is not in the
that the distribution of weights is Normal. Find a 95% interval.
confidence interval for the mean weight of all bags of
oranges. Use technology for your calculations.
a. Choose the correct interpretation of the confidence
interval below and, if necessary, fill in the answer boxes to
complete your choice.
b. Does the interval capture 10 pounds? Is there enough
evidence to reject the null hypothesis that the population
mean weight is 10 pounds? Explain your answer.
A random sample of 21 independent female college-aged Use http://www.sample-size.net/confidence-interval-mean/
dancers showed a sample mean height of 64.8 inches and
a sample standard deviation of 1.7 inches. Assume that a. We are 95% confident that the population mean height of female college-aged
this distribution of heights is Normal. dancers is between 64.0 and 65.6
a. Use technology to find a 95% confidence interval for the b. We are 99% confident that the population mean height of female college-aged
population mean height of dancers and interpret the dancers is between 63.7 and 65.9.
interval.
c. The 99% interval is wider because it has a greater confidence level, and therefore
b. Use technology to find a 99% confidence interval for the we use a bigger value of t*, which creates a wider interval
population mean height and interpret the interval.
c. Which interval is wider and why?
State whether each of the following changes would make a a. The interval will become wider.
confidence interval wider or narrower. (Assume that
nothing else changes.) b. The interval will become wider.
a. Changing from a 95% confidence level to a 99% c. The interval will become narrower.
confidence level.
b. Changing from a sample size of 300 to a sample size of
25.
c. Changing from a standard deviation of 25 pounds to a
standard deviation of 15 pounds.
Thirty GPAs from a randomly selected sample of statistics click the table icon, then the window icon, then command c. paste to:
students at a college are linked below. Assume that the http://www.calculatorsoup.com/calculators/statistics/mean-median-mode.php
population distribution is approximately Normal. The
technician in charge of records claimed that the population a. The sample mean is 3.10. It is higher than the population mean of 2.86.
mean GPA for the whole college is 2.86.
b. H0: μ=2.86
a. What is the sample mean? Is it higher or lower than the Ha: μ>2.86
population mean of 2.86?
(to find the test statistic and p-value, open in stat crunch[press table icon, window
b. The chair of the mathematics department claims that icon, open in stat chrunch], then compete a "One sample T hypothesis test" [stat, t-
statistics students typically have higher GPAs than the stat, one sample with data, compute])
typical college student. Use the four-step procedure and
the data provided to test this claim. Use a significance t=3.90
level of 0.05. Which of the following correctly states H0 p=0.000
and Ha?
Reject H0. The mean GPA for statistics students is significantly higher than 2.86.
