2022 Fall Semester Exam Review Statistics

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1

Here is some information about the first 10 U.S. presidents. Identify the individuals and variables in this data set. Classify each variable as categorical or quantitative.

Age at Inauguration
Age at Death
Name
Political Party
State of Birth

Categorical Variable
Quantitative Variable

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The dotplot below displays shows the scores of 21 Statistics students on a 20-point quiz.

What does one dot represent?

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1

The dotplot below displays shows the scores of 21 Statistics students on a 20-point quiz.

What percent of the dots show scores <18?

Then enter as a fraction, decimal proportion (Round to three places past the decimal) or as a percent.

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1

The dotplot below displays shows the scores of 21 Statistics students on a 20-point quiz.

a) Describe the shape of the distribution.
b) How does the mean compare to the median?

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1

The dotplot below displays shows the scores of 21 Statistics students on a 20-point quiz.

a) Using the dot plot above, what is the appropriate measure of center and spread?
b) Why would you choose these?

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1

Do you “binge-watch” television series by viewing multiple episodes of a series at one sitting? A survey of 800 people who “binge-watch” were asked how many episodes is too many to watch in one viewing session.
The results are displayed in the bar chart.

Explain how this graph is misleading.

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1

The dotplots show the total family income of 40 randomly chosen individuals each from Connecticut, Indiana, and Maine, based on U.S. Census data.

Which graph has a higher standard deviation?
ie. Which graph has greater variability?

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1

The dotplots show the total family income of 40 randomly chosen individuals each from Connecticut, Indiana, and Maine, based on U.S. Census data.

Which graph has a shape that is closest to being roughly symmetric?

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1

The dotplots show the total family income of 40 randomly chosen individuals each from Connecticut, Indiana, and Maine, based on U.S. Census data.

Which graph has the lowest mean?

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1

For a project in their statistics class, Alex and Tempe studied the impact of different types of background music on students’ ability to remember words from a list they were allowed to study for 5 min. Here is a list of how many words one group of students who listened to Beethoven’s Fifth Symphony were able to remember.
11   12   23   15   14   15   14   15
10   14   15   9   11   13   25   11
13   13   12   20   17   23   11   12
12   11   20   20   12   12   19   13
15   10   14   11   7   17   13   18

Use statsmedic.com/applets, 1 quantitative variable. Make a histogram that effectively displays the distribution of words recalled.
Describe the histogram using D.O.F.S.

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1

We used technology to compute the mean and median of this distribution.
One is 13 and the other is 14.3.
Based on the histogram, explain how you know which is which without doing any calculations.

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1

Using the same histogram from #10, what effect would removing the outliers have on the mean & standard deviation?

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1

Find the interquartile range of the data in #10.

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The standard deviation is 4.05. Interpret this value in context.

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Catherine and Ana suspect that athletes (i.e., students who have been on at least one varsity team) typically have a faster reaction time than other students. To test this theory, they gave an online reflex test to 33 varsity athletes at their school and 30 other students. The following parallel boxplots display the reaction times (in milliseconds) for the two groups of students.

What do the data suggest about Catherine and Ana’s suspicion? Explain.

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1

(1.9) The following dotplot gives the sale prices for 40 houses in Ames, Iowa, sold during a recent month. The mean sale price was $203,388 with a standard deviation of $87,609.

Find the percentile of the house that is indicated on the dotplot. Remember percentile means the percent to the LEFT of a value.

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(2.1) Researchers carried out a survey of fourth-, fifth-, and sixth-grade students in Michigan. Students were asked if good grades, athletic ability, or being popular was most important to them. The two-way table summarizes the survey data.

Use the table to calculate P(popular)
If you enter your answer as a decimal or percent, round to three places first.

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1

(2.1) Researchers carried out a survey of fourth-, fifth-, and sixth-grade students in Michigan. Students were asked if good grades, athletic ability, or being popular was most important to them. The two-way table summarizes the survey data.

Use the table to calculate P(popular|4th grade)
If you enter your answer as a decimal or percent, round to three places first.

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1

(2.1) Researchers carried out a survey of fourth-, fifth-, and sixth-grade students in Michigan. Students were asked if good grades, athletic ability, or being popular was most important to them. The two-way table summarizes the survey data.

Use the table to calculate P(popular|5th grade)
If you enter your answer as a decimal or percent, round to three places first.

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1

(2.1) Researchers carried out a survey of fourth-, fifth-, and sixth-grade students in Michigan. Students were asked if good grades, athletic ability, or being popular was most important to them. The two-way table summarizes the survey data.

Use the table to calculate P(popular|6th grade)
If you enter your answer as a decimal or percent, round to three places first.

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1

Based on your previous four answers, are being popular and grade level independent?
What relationship exists if there is one?

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1

(2.1) Researchers carried out a survey of fourth-, fifth-, and sixth-grade students in Michigan. Students were asked if good grades, athletic ability, or being popular was most important to them. The two-way table summarizes the survey data.

Use the table above to calculate P(5th grade or athletic)
If you enter your answer as a decimal or percent, round to three places first.

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1

(2.2, 2.3) At what age do babies learn to crawl? Does it take longer to learn in the winter, when babies are often bundled in clothes that restrict movement? There might even be an association between babies’ crawling age and the average temperature during the month when they first try to crawl (around 6 months after birth).
Data were collected from parents who reported the birth month and the age at which their child was first able to creep or crawl a distance of 4 feet within 1 minute. Information was obtained on 414 infants, 208 boys and 206 girls.
Average crawling age is given in weeks, and the average temperature (in degrees Fahrenheit) is for the month that is 6 months after the birth month.

Work with a partner, use statsmedic.com to make a scatterplot to display the relationship between average 6-month temperature and average crawling age. Use 2 quantitative variables.

Describe the relationship shown in the scatterplot.
Select all that apply.
If you're not sure of the strength, calculate the correlation.

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What does a correlation coefficient tell us?

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How would the correlation value change if the age of crawling was entered in days?

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3

Using your scatterplot from #25:

a) Describe what is unusual about the point representing May.

b) How does the point representing May affect the equation of the least-squares regression line? Explain.

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1

Using your scatterplot from #25, if the point representing May was removed, how would that affect the equation of the least-squares regression line? Explain.

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1

(2.3) The principal of a high school read a study that reported a positive correlation between the number of calculators owned by high school students and their math achievement. Based on this study, he decides to buy each student at his school 2 calculators, hoping to improve their math achievement.
Explain the flaw in the principal’s reasoning.

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1

(2.5) The scatterplot shows the relationship between latitude and mean July temperature (in degrees Fahrenheit) for 12 cities in the United States.
The equation of the regression line relating these variables is y -hat = 106.5 − 0.782x.

Predict the mean July temperature in Fairbanks, Alaska, at latitude 65º.
How confident are you in this prediction?

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1

Use the information from #25:
The equation of the regression line relating these variables is
July temperature -hat = 106.5 − 0.782(degrees latitude)

Los Angeles, California, is at latitude 34º and actually has a mean July temperature of 74º.
Calculate the predicted temperature value for July.
Keep all places past the decimal point, no units.

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1

Use the information from #25:
The equation of the regression line relating these variables is
July temperature -hat = 106.5 − 0.782(degrees latitude)

Los Angeles, California, is at latitude 34º and actually has a mean July temperature of 74º.

Calculate the residual for the July prediction. Keep all decimal points, no units.

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1

Use the information from #33:
Interpret the slope of the regression line.

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1

Use the information from #33:
Does the value of the y intercept have meaning in this context?
If so, interpret the y intercept. If not, explain why.

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1

We used a least-squares regression line to model the relationship between x = latitude
and y = mean July temperature (in degrees Fahrenheit) for a sample of 12 cities in the United States. Here is the residual plot for this model.

Explain what the residual plot suggests about the appropriateness of the linear model.

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(3.1) Indicate the following is a valid statistical question. Explain your reasoning.

'How many people visited Acadia National Park last Tuesday?'

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1

(3.1) Indicate if the following is a valid statistical question. Explain your reasoning.

'How many people visit Acadia National Park on a typical weekday in August?'

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1

(3.1) Indicate if the following is a valid statistical question. Explain your reasoning.

What proportion of soda bottles produced by a particular manufacturer on different days contain less soda than the label on the bottle indicates?'

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1

(3.1, 3.3, 3.4) A recent random sample of n = 805 adult U.S. residents found that the proportion who rated the honesty and ethical standards of nurses as very high or high is 0.85. This is 0.15 higher than the proportion recorded for doctors, the next highest-ranked profession.

Identify the sample and the population in this setting.

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1

Use #40:
Do you think that the proportion of all U.S. residents who rate the honesty and ethical standards of nurses as very high or high is exactly 0.85? Explain.

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1

Use #40:
If the size of a sample in the poll was increased to 1600 residents, what effect would this have on the variability? Explain.

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1

(3.2, 3.3) The administration at a high school with 1800 students wants to gather student opinion about parking for students on campus. It isn’t practical to contact all students.

Stand at the doors to the courtyard and by the bus drop off and survey students as they enter the school.
Number all students in the school, use a random number generator to draw 50 numbers, survey those corresponding students.
Send an email to all the students and ask them to fill out the survey online.

Voluntary Response Sample
Convenience Sample
Simple Random Sample (SRS)

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1

(3.3) Is flipping a flying disk as fair as flipping a coin? Hailey flips a disk 40 times and it lands right side up only 16 times. She suspects that the disk is more likely to land upside down. To determine if these data provide convincing evidence in support of Hailey’s conclusion, 100 trials of a simulation were conducted.
Each dot in the graph shows the number of right-side-up flips in a random sample of 40 flips, assuming that each flip has a 50% chance of landing right-side up.

Explain how the graph illustrates the concept of sampling variability.
Based on the results of the simulation, is there convincing evidence that flying disks are more likely to land upside down? Explain.

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1

(3.5) An opinion poll calls 2000 randomly chosen residential telephone numbers, then asks to speak with an adult member of the household.
The interviewer asks, “Box-office revenues are at an all-time high. How many movies have you watched in a movie theater in the past 12 months?”
In all, 1131 people responded. The researchers used the responses to estimate the mean number of movies adults have watched in a movie theater in the past 12 months.

Categorize the types of bias with the descriptions.

Wording of the question could cause people to be more likely to respond favorable
Using only residential phone numbers to contact the sample to be surveyed
2000 Randomly chosen phone numbers were called, response from 1131 people were received.

Response Bias
Undercoverage Bias
Nonresponse Bias

2022 Fall Semester Exam Review Statistics

Here is some information about the first 10 U.S. presidents. Identify the individuals and variables in this data set. Classify each variable as categorical or quantitative.

The dotplot below displays shows the scores of 21 Statistics students on a 20-point quiz.What does one dot represent?

The dotplot below displays shows the scores of 21 Statistics students on a 20-point quiz.What percent of the dots show scores <18?Then enter as a fraction, decimal proportion (Round to three places past the decimal) or as a percent.

The dotplot below displays shows the scores of 21 Statistics students on a 20-point quiz.a) Describe the shape of the distribution.b) How does the mean compare to the median?

The dotplot below displays shows the scores of 21 Statistics students on a 20-point quiz.a) Using the dot plot above, what is the appropriate measure of center and spread?b) Why would you choose these?

The dotplots show the total family income of 40 randomly chosen individuals each from Connecticut, Indiana, and Maine, based on U.S. Census data. Which graph has a higher standard deviation?ie. Which graph has greater variability?

The dotplots show the total family income of 40 randomly chosen individuals each from Connecticut, Indiana, and Maine, based on U.S. Census data. Which graph has a shape that is closest to being roughly symmetric?

The dotplots show the total family income of 40 randomly chosen individuals each from Connecticut, Indiana, and Maine, based on U.S. Census data. Which graph has the lowest mean?

We used technology to compute the mean and median of this distribution. One is 13 and the other is 14.3. Based on the histogram, explain how you know which is which without doing any calculations.

Using the same histogram from #10, what effect would removing the outliers have on the mean & standard deviation?

Find the interquartile range of the data in #10.

The standard deviation is 4.05. Interpret this value in context.

Based on your previous four answers, are being popular and grade level independent?What relationship exists if there is one?

What does a correlation coefficient tell us?

How would the correlation value change if the age of crawling was entered in days?

Using your scatterplot from #25:a) Describe what is unusual about the point representing May.b) How does the point representing May affect the equation of the least-squares regression line? Explain.

Using your scatterplot from #25, if the point representing May was removed, how would that affect the equation of the least-squares regression line? Explain.

Use the information from #33:Interpret the slope of the regression line.

Use the information from #33:Does the value of the y intercept have meaning in this context? If so, interpret the y intercept. If not, explain why.

(3.1) Indicate the following is a valid statistical question. Explain your reasoning.'How many people visited Acadia National Park last Tuesday?'

(3.1) Indicate if the following is a valid statistical question. Explain your reasoning.'How many people visit Acadia National Park on a typical weekday in August?'

(3.1) Indicate if the following is a valid statistical question. Explain your reasoning.What proportion of soda bottles produced by a particular manufacturer on different days contain less soda than the label on the bottle indicates?'

Use #40:Do you think that the proportion of all U.S. residents who rate the honesty and ethical standards of nurses as very high or high is exactly 0.85? Explain.

Use #40:If the size of a sample in the poll was increased to 1600 residents, what effect would this have on the variability? Explain.

(3.2, 3.3) The administration at a high school with 1800 students wants to gather student opinion about parking for students on campus. It isn’t practical to contact all students.

Here is some information about the first 10 U.S. presidents. Identify the individuals and variables in this data set. Classify each variable as categorical or quantitative.

The dotplot below displays shows the scores of 21 Statistics students on a 20-point quiz.What does one dot represent?

The dotplot below displays shows the scores of 21 Statistics students on a 20-point quiz.What percent of the dots show scores <18?Then enter as a fraction, decimal proportion (Round to three places past the decimal) or as a percent.

The dotplot below displays shows the scores of 21 Statistics students on a 20-point quiz.a) Describe the shape of the distribution.b) How does the mean compare to the median?

The dotplot below displays shows the scores of 21 Statistics students on a 20-point quiz.a) Using the dot plot above, what is the appropriate measure of center and spread?b) Why would you choose these?

The dotplots show the total family income of 40 randomly chosen individuals each from Connecticut, Indiana, and Maine, based on U.S. Census data. Which graph has a higher standard deviation?ie. Which graph has greater variability?

The dotplots show the total family income of 40 randomly chosen individuals each from Connecticut, Indiana, and Maine, based on U.S. Census data. Which graph has a shape that is closest to being roughly symmetric?

The dotplots show the total family income of 40 randomly chosen individuals each from Connecticut, Indiana, and Maine, based on U.S. Census data. Which graph has the lowest mean?

We used technology to compute the mean and median of this distribution. One is 13 and the other is 14.3. Based on the histogram, explain how you know which is which without doing any calculations.

Using the same histogram from #10, what effect would removing the outliers have on the mean & standard deviation?

Find the interquartile range of the data in #10.

The standard deviation is 4.05. Interpret this value in context.

Based on your previous four answers, are being popular and grade level independent?What relationship exists if there is one?

What does a correlation coefficient tell us?

How would the correlation value change if the age of crawling was entered in days?

Using your scatterplot from #25:a) Describe what is unusual about the point representing May.b) How does the point representing May affect the equation of the least-squares regression line? Explain.

Using your scatterplot from #25, if the point representing May was removed, how would that affect the equation of the least-squares regression line? Explain.

Use the information from #33:Interpret the slope of the regression line.

Use the information from #33:Does the value of the y intercept have meaning in this context? If so, interpret the y intercept. If not, explain why.

(3.1) Indicate the following is a valid statistical question. Explain your reasoning.'How many people visited Acadia National Park last Tuesday?'

(3.1) Indicate if the following is a valid statistical question. Explain your reasoning.'How many people visit Acadia National Park on a typical weekday in August?'

(3.1) Indicate if the following is a valid statistical question. Explain your reasoning.What proportion of soda bottles produced by a particular manufacturer on different days contain less soda than the label on the bottle indicates?'

Use #40:Do you think that the proportion of all U.S. residents who rate the honesty and ethical standards of nurses as very high or high is exactly 0.85? Explain.

Use #40:If the size of a sample in the poll was increased to 1600 residents, what effect would this have on the variability? Explain.

(3.2, 3.3) The administration at a high school with 1800 students wants to gather student opinion about parking for students on campus. It isn’t practical to contact all students.

The dotplot below displays shows the scores of 21 Statistics students on a 20-point quiz.

What does one dot represent?

The dotplot below displays shows the scores of 21 Statistics students on a 20-point quiz.

What percent of the dots show scores <18?

Then enter as a fraction, decimal proportion (Round to three places past the decimal) or as a percent.

The dotplot below displays shows the scores of 21 Statistics students on a 20-point quiz.

a) Describe the shape of the distribution.
b) How does the mean compare to the median?

The dotplot below displays shows the scores of 21 Statistics students on a 20-point quiz.

a) Using the dot plot above, what is the appropriate measure of center and spread?
b) Why would you choose these?

The dotplots show the total family income of 40 randomly chosen individuals each from Connecticut, Indiana, and Maine, based on U.S. Census data.

Which graph has a higher standard deviation?
ie. Which graph has greater variability?

The dotplots show the total family income of 40 randomly chosen individuals each from Connecticut, Indiana, and Maine, based on U.S. Census data.

Which graph has a shape that is closest to being roughly symmetric?

The dotplots show the total family income of 40 randomly chosen individuals each from Connecticut, Indiana, and Maine, based on U.S. Census data.

Which graph has the lowest mean?

We used technology to compute the mean and median of this distribution.
One is 13 and the other is 14.3.
Based on the histogram, explain how you know which is which without doing any calculations.

Based on your previous four answers, are being popular and grade level independent?
What relationship exists if there is one?

Using your scatterplot from #25:

a) Describe what is unusual about the point representing May.

b) How does the point representing May affect the equation of the least-squares regression line? Explain.

Use the information from #33:
Interpret the slope of the regression line.

Use the information from #33:
Does the value of the y intercept have meaning in this context?
If so, interpret the y intercept. If not, explain why.

(3.1) Indicate the following is a valid statistical question. Explain your reasoning.

'How many people visited Acadia National Park last Tuesday?'

(3.1) Indicate if the following is a valid statistical question. Explain your reasoning.

'How many people visit Acadia National Park on a typical weekday in August?'

(3.1) Indicate if the following is a valid statistical question. Explain your reasoning.

What proportion of soda bottles produced by a particular manufacturer on different days contain less soda than the label on the bottle indicates?'

Use #40:
Do you think that the proportion of all U.S. residents who rate the honesty and ethical standards of nurses as very high or high is exactly 0.85? Explain.

Use #40:
If the size of a sample in the poll was increased to 1600 residents, what effect would this have on the variability? Explain.

The dotplot below displays shows the scores of 21 Statistics students on a 20-point quiz.

What does one dot represent?

The dotplot below displays shows the scores of 21 Statistics students on a 20-point quiz.

What percent of the dots show scores <18?

Then enter as a fraction, decimal proportion (Round to three places past the decimal) or as a percent.

The dotplot below displays shows the scores of 21 Statistics students on a 20-point quiz.

a) Describe the shape of the distribution.
b) How does the mean compare to the median?

The dotplot below displays shows the scores of 21 Statistics students on a 20-point quiz.

a) Using the dot plot above, what is the appropriate measure of center and spread?
b) Why would you choose these?

The dotplots show the total family income of 40 randomly chosen individuals each from Connecticut, Indiana, and Maine, based on U.S. Census data.

Which graph has a higher standard deviation?
ie. Which graph has greater variability?

The dotplots show the total family income of 40 randomly chosen individuals each from Connecticut, Indiana, and Maine, based on U.S. Census data.

Which graph has a shape that is closest to being roughly symmetric?

The dotplots show the total family income of 40 randomly chosen individuals each from Connecticut, Indiana, and Maine, based on U.S. Census data.

Which graph has the lowest mean?

We used technology to compute the mean and median of this distribution.
One is 13 and the other is 14.3.
Based on the histogram, explain how you know which is which without doing any calculations.

Based on your previous four answers, are being popular and grade level independent?
What relationship exists if there is one?

Using your scatterplot from #25:

a) Describe what is unusual about the point representing May.

b) How does the point representing May affect the equation of the least-squares regression line? Explain.

Use the information from #33:
Interpret the slope of the regression line.

Use the information from #33:
Does the value of the y intercept have meaning in this context?
If so, interpret the y intercept. If not, explain why.

(3.1) Indicate the following is a valid statistical question. Explain your reasoning.

'How many people visited Acadia National Park last Tuesday?'

(3.1) Indicate if the following is a valid statistical question. Explain your reasoning.

'How many people visit Acadia National Park on a typical weekday in August?'

(3.1) Indicate if the following is a valid statistical question. Explain your reasoning.

What proportion of soda bottles produced by a particular manufacturer on different days contain less soda than the label on the bottle indicates?'

Use #40:
Do you think that the proportion of all U.S. residents who rate the honesty and ethical standards of nurses as very high or high is exactly 0.85? Explain.

Use #40:
If the size of a sample in the poll was increased to 1600 residents, what effect would this have on the variability? Explain.