stats exam 2, all right

In 2006, the General Social Survey asked, "In the past 12 months, have you experienced back pain?." For this question, 475 people said that they did out of 1723 randomly selected people. What is the 95% confidence interval for the proportion of all Americans that have experienced back pain in the past 12 months?

(0.255, 0.297)

A random sample of 5 homes in Newberry, Florida had a mean of $169,900 and a standard deviation of $21,756. Construct a 95% confidence interval for the average home of this size in Newberry.

(142886, 196914)

A study on students drinking habits asks a random sample of 124 "non-greek" UF students how many alcoholic beverages they have consumed in the past week. The sample reveals an average of 3.66 alcoholic drinks, with a standard deviation of 2.82. Construct a 90% confidence interval for the true average number of alcoholic drinks all UF "non-greek" students have in a one week period.

(3.24, 4.08)

A random sample of 10 recent college graduates found that starting salaries for accountants in New York City had a mean of $47,589 and a standard deviation of $11,364. Construct a 95% confidence interval for the average starting salary of all accountants in the city.

(39460.25, 55717.75)

A random sample of 8 recent college graduates found that starting salaries for computer scientists had a mean of $85000 and a standard deviation of $15000. Construct a 95% confidence interval for the average starting salary of all computer scientists in Gainesville.

(72460, 97540)

Suppose that you were trying to determine if the population proportion of Americans that currently believe that nuclear power is extremely/very dangerous to the environment was less than 50%. You decide to test the null hypothesis Ho: p = 0.50 versus Ha: p < 0.50. In 1993, the General Social Survey included a question that asked its participants if they felt that nuclear power plants were extremely/very dangerous to the environment. Out of the 1419 surveyed, 630 said yes. What is the value of the test statistic for this problem?

-4.22

n 2004, the General Social Survey (which uses a method similar to simple random sampling) asked, "Do you consider yourself athletic?" For this question, 255 people said that that they did out of 2373 randomly selected people. What is the standard error of the confidence interval?

0.0064

In 2004, the General Social Survey (which uses a method similar to simple random sampling) asked, "Do you consider yourself athletic?" For this question, 255 people said that that they did out of 2373 randomly selected people. We will make a 99% confidence interval for p. What is the margin of error of the confidence interval?

0.0164

For a test of Ho: p = 0.5, the z test statistic equals 1.74. Find the p-value for Ha: p > 0.5.

0.0409

For a test of Ho: p = 0.5, the z test statistic equals 1.52. Find the p-value for Ha: p > 0.5.

0.0643

Twenty-nine percent of Americans say they are confident that passenger trips to the moon will occur in their lifetime. You randomly sample 200 Americans and ask if they believe passenger trips to the moon will occur in their lifetime. What is the probability that less than 25% of the people sampled will answer Yes to the question?

0.106

A water treatment plant needs to maintain the pH of the water in the reservoir at a certain level. To monitor this, they take 2 oz. of water at 37 locations every hour, measure the pH at each of those locations, and find their average. If the pH level of the reservoir is ok, the results at each location will have varying results, with an average pH of 8.5 and a standard deviation of 0.22. If the pH level of the reservoir is ok, what is the probability that the sample average is LESS than 8.47?

0.2033

Suppose that you were trying to determine if out of the Americans that smoke, the proportion that have tried to quit was more than 75%. You decide to test the null hypothesis Ho: p = 0.75 versus Ha: p > 0.75. In 1993, the General Social Survey had a question that asked its participants (that currently smoked) if they had ever tried to quit smoking. Out of 288, 218 said yes, they had tried to quit smoking. What is the value of the test statistic for this problem?

0.272

In 1996, the General Social Survey asked, "On the whole, do you think it should be the governments responsibility to provide industry with the help that it needs to grow?" For this question, 206 people said that it definitely should out of 1572 randomly selected people. The General Social survey randomly selects adults living in the US. Someone wanted to compute a 95% confidence interval for p. Are the values for phat and p known?

phat is known. It is equal to 206/1572 = 0.13, p is unknown

In 1987, the General Social Survey asked, "Have you ever been active in a veteran's group? " For this question, 52 people said that they did out of 98 randomly selected people. The General Social survey randomly selects adults living in the US. Someone wanted to compute a 95% confidence interval for p. Are the values for phat and p known?

phat is known. It is equal to 52/98 = 0.53, p is unknown

A study on students drinking habits wants to determine the true average number of alcoholic drinks all FSU undergraduate students who are members of a fraternity or sorority have in a one week period. We know from preliminary studies that the standard deviation is around 2.6. How many students should be sampled to be within 0.25 drinks of population mean with 95% probability?

416

Suppose you conduct a test and your p-value is equal to 0.016. What can you conclude?

Reject Ho at alpha=0.05 but not at alpha=0.01 REMEMBER: Reject Ho if the p-value less than alpha.

Suppose you conduct a test, and your p-value is equal to 0.06. What can you conclude?

Reject Ho at alpha=0.10 but not at alpha =0.05 REMEMBER: Reject Ho if the p-value less than alpha.

The distribution of the amount of money in savings accounts for University of Florida students has an average of 300 dollars and a standard deviation of 1,000. Suppose that we take a random sample of 10 UF students and ask them how much they have in their savings account. The sampling distribution of the sample mean amount of money in a savings account is

not Approximately Normal

The distribution of the amount of money in savings accounts for University of Alabama students has an average of 950 dollars and a standard deviation of 1,000 dollars. Suppose that we take a random sample of 4 University of Alabama students and ask them how much they have in their savings account. The sampling distribution of the sample mean amount of money in a savings account is

not approximately normal

The distribution of the amount of money in savings accounts for University of Miami students has an average of 1,100 dollars and a standard deviation of 1000 dollars. Suppose that we take a random sample of 10 University of Miami students and ask them how much they have in their savings account. The sampling distribution of the sample mean amount of money in a savings account is

not approximately normal

Which of the following are assumptions for the Significance Test for the Proportion?

npopo and n(1-popo) are both greater than 15 Data is Categorical. Data is from a random sample.

What is the mean of the sampling distribution of the sample proportion?

p

In order for a constitutional amendment to the Florida constitution to pass 60% of the popular vote must support the amendment. A researcher is interested in determining if the more than sixty percent of the voters would support a new amendment about higher education. The researcher asks 500 random selected potential voters if they would support the amendment. Define the parameter.

p = the population proportion of Floridians that would support the amendment.

A water treatment plant needs to maintain the pH of the water in the reservoir at a certain level. To monitor this, they take 2 oz. of water at 37 locations every hour, measure the pH at each of those locations, and find their average. If the pH level of the reservoir is ok, the results at each location will have varying results, with an average pH of 8.5 and a standard deviation of 0.22. If the pH level of the reservoir is ok, what is the probability that the sample average is MORE than 8.40?

0.6736

When computing a bootstrap confidence interval for a parameter, at least how many times should we re-sample from the original sample?

1,000

What value of z should we use when making a 91% confidence interval for p?

1.70

A study reports that college students work, on average, between 4.63 and 12.63 hours a week, with confidence coefficient .95. Which of the following statements are correct? MARK ALL THAT ARE TRUE. There are four correct answers. You must mark them all to get credit.

95% of samples will produce intervals that contain mu. The probability that mu is included in a 95% CI is 0.95. The interval was produced by a technique that captures mu 95% of the time. We are 95% confident that the population mean time that college students work is between 4.63 and 12.63 hours a week.

A researcher is interested in determining if a psychic really has power to predict. The researcher takes six pictures of famous cartoon characters. After mixing the pictures up many times, the researcher selects one picture, but doesn't show the psychic. The psychic is asked to predict which picture the researcher selected. The researcher records if the psychic was correct or not. The researcher does this one hundred times. If the psychic really has special abilities then he should the cartoon character more often then if it was by chance alone. The researcher is interested in determining if the correct character is selected significantly more often then chance would suggest. What would be the null and alternative hypothesis for this case?

Answer: Ho: p = 1/6 Ha: p >1/6 Why: Hypothesis statements are about the population proportion(p), not the sample proportion (p-hat).By just random chance, someone would pick the cup with the ball under it 1/3 of the time. The researcher in this case is interested in determining if the ball is selected more often then suggested by chance.

Suppose you conduct a test and your p-value is equal to 0.02. What can you conclude?

Reject Ho at alpha=0.05 but not at alpha=0.01

When we make inferences about ONE POPULATION PROPORTION, what assumptions do we need to make? Mark all that apply.

Data must be from a simple random sample. Data is categorical. Counts of successes and failures at least 15 each.

Suppose you conduct a test and your p-value is equal to 0.93. What can you conclude?

Do not reject Ho at alpha equal to 0.10, 0.05, or 0.01

To find the 95% confidence interval for the population standard deviation using the bootstrap method. You repeatedly sample with replacement from the sample, tens of thousands of times. For each sample, you compute the sample standard deviation. What is the next step?

Find the 2.5th and 97.5th percentiles of these values.

A researcher is interested in determining if a psychic really has power to predict. The researcher takes four cards, each of a different type: king, queen, jack, and ace. After mixing up the cards many times and he selects one card without showing the psychic. The researcher asks the psychic which card was selected. The researcher records if the psychic was correct or not. The researcher does this two hundred times. If the psychic really has special abilities then he should pick the correct card more often then if it was by chance alone. The researcher is interested in determining if the card was identified correctly significantly more often then chance would suggest. What would be the null and alternative hypothesis for this case?

Ho: p = 0.25 Ha: p >0.25 why: Hypothesis statements are about the population proportion(p), not the sample proportion (p-hat).By just random chance, someone would identify the card 1/4 of the time. The researcher in this case is interested in determining if the card is identified more often then suggested by chance.

Go to artofstat.com, click on WebApps and open the Sampling Distribution for the Sample Mean for continuous variables (NOT discrete). Under Select Population Distribution, choose Skewed from the drop down menu. A graph is displayed. What values does this graph represent?

It represents all the observations in the population.

Minute Maid states that a bottle of juice contains 473 mL. Consumer groups are interested in determining if the bottles contain less than the amount stated on the label. To test their claim, they sample 30 bottles. The sample mean was 472mL and the standard deviation is 0.2. What does mu represent here?

The average contents of all bottles of juice in the population, which is unknown.

A sample of 15 recent college graduates found that starting salaries for attorneys in New York City had a mean of $102,342 and a standard deviation of $21,756. What does mu represent?

The average salary of all recently graduated attorneys in New York City, which is unknown.

On the Sampling Distribution for the Sample Proportion app in artofstat.com, Select Population Proportion (p) to be 0.8. Keep the sample size (n) at 50. Under Select how many samples (of size n) you want to simulate drawing from the population, CHANGE this to 10,000 samples. Click on Draw Sample(s) ONCE. Imagine we are conducting surveys and a success is a particular person answering Yes to our question. Look at the bottom graph with the Sampling Distribution of the Sample Proportion. What does it represent?

The proportion of Yesses computed from each of 10,000 random samples of 50 people.

On the Sampling Distribution for the Sample Mean (continuous var) app in artofstat.com, under Select Population Distribution, choose Skewed from the drop down menu. Under "Select sample size (n)" the default is 20. Under "Select how many samples (of size n) you want to simulate drawing from the population", make sure the button with 1 sample is selected. Now click on Draw Sample(s) - two new graphs will appear. On the middle graph labeled Data Distribution there is a histogram, a blue triangle labeled x-bar and a red circle labeled mu. Now click AGAIN on Draw Sample(s) a FEW times and notice what happens to x-bar and mu. Also notice that each time you draw a sample a new point gets added to the bottom graph. Which of the following statements is correct?

The values of x-bar vary around the value of mu.

One of the reasons to use the bootstrap method is because the formula for the confidence interval is too hard to derive.

True

A sampling distribution refers to the distribution of:

a sample statistic

What is the mean of the sampling distribution of the sample mean?

mu

What is the standard error of the sampling distribution of sample proportion?

sqrt(p(1-p)/n)

On the Sampling Distribution for the Sample Proportion app in artofstat.com, Select Population Proportion (p) to be 0.1. Keep the sample size (n) at 10. Under Select how many samples (of size n) you want to simulate drawing from the population, CHANGE this to 10,000 samples. Click on Draw Sample(s) ONCE. Notice the center, spread and shape of the distribution. Change the value of p by increments of 0.1 (0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7. 0.8, 0.9, 1.0). What happens to the symmetry as p increases

It is more symmetric close to 0.5 and more skewed close to 0 and 1.

If "np is greater than or equal to 15" and "n(1-p) is greater than or equal to 15", what is the approximate shape of the sampling distribution of the sample proportion?

Normal

As of January 2017, the population distribution of physician's assistance salaries in Boca Raton was right skewed with a mean of $98347. Which of the following statements are true?

The sampling distribution of the sample mean (n=50) would be bell shaped.

Suppose that ten bats was used in the experiment. For each trail, the zoo keeper pointed to one of two "feeders". Suppose that the bats went to the correct feeder (the one that the zoo keeper pointed at) 8 times. What would be the population proportion of times that bats would follow the point?

Unknown

In 1996, the General Social Survey asked, "On the whole, do you think it should be the governments responsibility to give financial assistance to college students from low income families?" For this question, 428 people said that it definitely should out of 1572 randomly selected people. What is the 95% confidence interval for the proportion of all Americans that believe it is the government's responsibility?

(0.260, 0.283)

In 2006, the General Social Survey asked, "Do you see yourself as someone who has an active imagination?" For this question, 448 people said that they definitely did out of 1506 randomly selected people. What is the 95% confidence interval for the proportion of all Americans who believe that believe that they have an active imagination?

(0.274, 0.321)

Suppose that twelve bats was used in the experiment. For each trail, the zoo keeper pointed to one of two "feeders". Suppose that the bats went to the correct feeder (the one that the zoo keeper pointed at) 9 times. Find the 95% confidence interval for the population proportion of times that the bats would follow the point.

(0.46, 0.91)

In 1996, the General Social Survey (which uses a method similar to simple random sampling) asked, "On the whole, do you think it should be the government's responsibility to provide decent housing for those who can't afford it?" For this question, 240 people said that it definitely should out of 1572 randomly selected people. What is the standard error of the confidence interval?

0.0091

You want to make a confidence interval for the true average rainfall in September in Gainesville. A random sample of 5 days reveals the following rainfall amounts: 0 0 0.77 1.37 0.08 What is the standard error of the sample mean, x-bar? IMPORTANT: Keep all significant digits in your calculator until the very end.

0.273

Nine percent of Americans say they are well informed about politics in comparison to most people. You randomly sample 200 Americans and ask if they believe that they are well informed about politics in comparison to most people. What is the probability that less than 8% of the people sampled will answer Yes to the question?

0.3121

You want to make a confidence interval for the true average temperature at noon in September in Gainesville. A random sample of 6 days reveals the following temperatures: 77 77 77 75 75 76 What is the standard error of the sample mean, x-bar? IMPORTANT: Keep all significant digits in your calculator until the very end.

0.4013

Nine percent of Americans say they are well informed about politics in comparison to most people. You randomly sample 200 Americans and ask if they believe that they are well informed about politics in comparison to most people. What is the probability that less than 10% of the people sampled will answer Yes to the question?

0.6894 WHY: this is the probability that more than 10% say that they are well informed about politics in comparison to other people. Remember that np and n(1-p) must be greater than or equal to 15 for you to be able to complete the problem. Draw the picture. Mark off the mean and the value of interest. Create a z-score. (phat - p)/sqrt(p(1-p)/n). Use the z-score and the z-table to find the correct probability.

A water treatment plant needs to maintain the pH of the water in the reservoir at a certain level. To monitor this, they take 2 oz. of water at 37 locations every hour, measure the pH at each of those locations, and find their average. If the pH level of the reservoir is ok, the results at each location will have varying results, with an average pH of 8.5 and a standard deviation of 0.22. If the pH level of the reservoir is ok, what is the probability that the sample average is MORE than 8.42?

0.9868

What value of z should we use when making a 93% confidence interval for p?

1.81

On the Sampling Distribution for the Sample Mean (continuous var) app in artofstat.com, under Select Population Distribution, choose Skewed from the drop down menu. Under "Select sample size (n)" the default is 20. Under Select how many samples (of size n) you want to simulate drawing from the population, CHANGE this to 10,000 samples. Click on Draw Sample(s) ONCE. Imagine we are collecting data on people's salaries. Look at the bottom graph with the Sampling Distribution of the Sample Mean. What does it represent?

10,000 averages of the salaries of 20 people in each sample.

You want to make a confidence interval for the true average number of users per day of the Real Player server at UF. A random sample of 8 days reveals the following numbers: 4593 5197 3865 4835 3900 3171 3559 18091 What is the standard error of the sample mean, x-bar? IMPORTANT: Keep all significant digits in your calculator until the very end.

1757.77

What value of z should we use when making a 98% confidence interval for p?

2.33

Suppose that you were trying to determine if the population proportion of Americans that smoked that have tried to quit was more than 60%. You decide to test the null hypothesis Ho: p = 0.60 versus Ha: p > 0.60. In 1990, the General Social Survey had a question that asked its participants (that currently smoked) if they had ever tried to quit smoking.Out of 284, 211 said yes, they had tried to quit smoking. What is the value of the test statistic for this problem?

4.92 why: This question is asking for the test statistic only. TS = (phat - po )/ stderr. The stderr is sqrt(po*(1-po)/ n).

A study on students drinking habits wants to determine the true average number of alcoholic drinks all UF "greek" students have in a one week period. We know from preliminary studies that the standard deviation is around 6.3. How many students should be sampled to be within 0.5 drink of population mean with 95% probability?

610

About 30% of people age 50 to 60 suffer from mild depression. A researcher is interested in determining if a vitamin D supplement will increase or decrease the proportion of people that have mild depression. The researcher randomly selects 500 people between the ages of 50 and 60 and ask them to take a vitamin D supplement for 6 months. At the end of the six months, the participants are asked to complete a survey. A psychologist then classifies each participant as either depressed or not. The psychologist classifies 158 people as depressed. Is the proportion of people that are classified as depressed different from 0.30? What is the null and alternative hypothesis?

Ho: p =0.30 Ha: p does not equal 0.30

On the Sampling Distribution for the Sample Mean (continuous var) app in artofstat.com, under Select Population Distribution, choose Bimodal from the drop down menu. Under "Select sample size (n)" change the sample size to 2. Under Select how many samples (of size n) you want to simulate drawing from the population, CHANGE this to 10,000 samples. Click on Draw Sample(s) ONCE. Look at the bottom graph with the Sampling Distribution of the Sample Mean. Now, look at the following sample sizes 5, 10, 15, and 40. What happens overall to the shape of the sampling distribution of the sample mean as n was increased?

It becomes more Normal.

Go to artofstat.com, click on WebApps and open the Explore Coverage app. Change the tab on top of the graph to Confidence Interval for a Mean. Change the Population Distribution to Bell-shaped and use the default mean=50 and standard deviation=10. Under "Choose confidence level (in %)" set it at 95% the default. Under "Select sample size (n)" use n=10. Under "Select how many samples (of size n) you want to draw from the population" select 100. Click on "Draw sample(s)" and note that 100 confidence intervals appear under the population graph. Go back and change the sample size to n = 25. What happens to the width of the interval as the sample size increases from n = 10 to n = 25?

It decreases.

On the Sampling Distribution for the Sample Mean (continuous var) app in artofstat.com, under Select Population Distribution, choose Bimodal from the drop down menu. Under "Select sample size (n)" change the sample size to 2. Under Select how many samples (of size n) you want to simulate drawing from the population, CHANGE this to 10,000 samples. Click on Draw Sample(s) ONCE. Look at the bottom graph with the Sampling Distribution of the Sample Mean. Now, look at the following sample sizes 5, 10, 15, and 40. What happens overall to the standard deviation of the sampling distribution of the sample mean as n was increased?

It decreases.

On the Sampling Distribution for the Sample Proportion app in artofstat.com, Select Population Proportion (p) to be 0.9. Keep the sample size this value of p for the whole question. Under Select how many samples (of size n) you want to simulate drawing from the population, CHANGE this to 10,000 samples. Click on Draw Sample(s) ONCE. Notice the center, spread and shape of the distribution. Change the value of n by increments of 10 (10, 20, 30, 40, 50, 60, 70, 80, 90, 100). What happens to the standard deviation of phat as n increases?

It decreases.

Go to artofstat.com, click on WebApps and open the Explore Coverage app. Change the tab on top of the graph to Confidence Interval for a Mean. Change the Population Distribution to Bell-shaped and use the default mean=50 and standard deviation=10. Under "Choose confidence level (in %)" set it at 90%. Under "Select sample size (n)" use the default of n=20. Under "Select how many samples (of size n) you want to draw from the population" select 100. Click on "Draw sample(s)" and note that one hundred confidence intervals appear under the population graph. Go back and change the confidence levels to 95% and then to 99%. What happens to the coverage as the confidence level increases from 90% to 99%?

It increases.

You want to make a confidence interval for the true average number of users of the video server at UF. A random sample of 8 days reveals the following numbers: 4593, 5197, 3865, 4835, 3900, 3171, 3559, 18091 Can we use the t table to make this confidence interval?

No, since a plot of the data shows an outlier.

If n is greater than 30 or if the original population is normally distributed, what is the approximate shape of the sampling distribution of the sample mean?

Normal

What proportion of students who take Intro Stats at the University of Florida have never taken Statistics before? Is it more than half of them? A study of STA 2122 students found that 438 out of 654 students had never taken a Statistics course before. Match the following symbols with the correct answer.

P = Parameters we wish to make inferences about p-hat = estimator used.

A coffee company wants to make sure that their coffee is being served at the right temperature. If it is too hot, the customers could burn themselves. If it is too cold, the customers will be unsatisfied. The company has determined that they want the average coffee temperature to be 65 degrees C. They take a sample of 20 orders of coffee and find the sample mean to be equal to 70.2 C. What does mu represent for this problem?

The average temperature of coffee in the population, which is unknown.

On the Sampling Distribution for the Sample Mean (continuous var) app in artofstat.com, under Select Population Distribution, choose Skewed from the drop down menu. Under "Select sample size (n)" the default is 20. Under "Select how many samples (of size n) you want to simulate drawing from the population", make sure the button with 1 sample is selected. Now click on Draw Sample(s) - two new graphs will appear. On the middle graph labeled Data Distribution there is a histogram, a blue triangle labeled x-bar and a red circle labeled mu. Which of the following statements is true?

The sample mean, x-bar, was computed from all the values in the histogram.

Go to artofstat.com, click on WebApps and open the Explore Coverage app. Change the tab on top of the graph to Confidence Interval for a Mean. Change the Population Distribution to Bell-shaped and use the default mean=50 and standard deviation=10. Under "Choose confidence level (in %)" use the default 95, and under "Select sample size (n)" use the default of n=20. Under "Select how many samples (of size n) you want to draw from the population" start with just 1. Click on "Draw sample(s)" and note that a confidence interval appears under the population graph. What does the red half circle at the bottom of the page represent?

The true population mean, which does not change each time we take a sample.

On the Sampling Distribution for the Sample Proportion app in artofstat.com, Select Population Proportion (p) to be 0.8. Keep the sample size (n) at 50. Under Select how many samples (of size n) you want to simulate drawing from the population, make sure the button with 1 sample is selected. Now click on Draw Sample(s) - two new graphs will appear. On the middle graph, look at the p-hat denoted by a blue triangle and the p denoted by a red circle. Now click AGAIN on Draw Sample(s) a FEW times and notice what happens to p-hat and p. Also notice that each time you draw a sample a new point gets added to the bottom graph. Which of the following statements is correct?

The values of p-hat vary around the value of p.

Suppose that a survey was taken of 320 people and each person was asked if they approved or disapproved of the president's actions during the government shutdown. One hundred eighty people said that they approved. Which of the following statements correctly describes how the confidence interval for the population proportion of people that approved the President's actions during the government shutdown?

There are at least 15 successes and 15 failures. A large sample confidence interval for the population proportion can be computed (phat +/- z * sqrt(p*(1-p)/n) with no additional values added.

Suppose that 12 bats were used in the experiment. For each trail, the zoo keeper pointed to one of two "feeders". Suppose that the bats went to the correct feeder (the one that the zoo keeper point at) 8 times. What would be the population proportion of number of times that bats would follow the point?

Unknown

If the assumptions for the large sample confidence interval for the population proportion are not met, what adjustments can be made?

Use phat = (X+2)/(N+4) instead.

In the same study, a zoo keeper pointed to one of two "feeders". It was recorded whether or not the bats followed the point and went to the correct feeder. (Assume that all of the assumptions are met.) A 95% confidence interval for p was found to be (0.53, 0.67). Interpret.

We are 95% confident that the population proportion of times that bats follow the point and go to the correct feeder is between 0.53 and 0.67.

Why in this case would we expect the sample size to be small? (Mark all that might apply.)

We wouldn't want to unnecessarily stress the animals. There is a limited number of bats in captivity. There is a limited amount of time that bat keepers maybe able to devote to this activity.

Go to artofstat.com, click on WebApps and open the Sampling Distribution for the Sample Proportion app. Under Select Population Proportion (p) change it to 0.1. Note the height of the bar for Success (1) is the same as your value of p, so the height of the bar for Failures (0) has to be 1-p. This value of p represents:

a parameter - the true proportion of successes in the entire population. WHY: Think of the symbol p - what does it represent?

On the Sampling Distribution for the Sample Proportion app in artofstat.com, Select Population Proportion (p) to be 0.1. Keep the sample size (n) at 50. Under Select how many samples (of size n) you want to simulate drawing from the population, make sure the button with 1 sample is selected. Now click on Draw Sample(s) - two new graphs will appear. On the middle graph, look at the p-hat denoted by a blue triangle. This value represents:

a statistic or estimator - the proportion of successes computed for the sample. WHY: Think of the symbol p-hat, what does it represent?

Suppose 60% of American adults believe Martha Stewart is guilty of obstruction of justice and fraud related to insider trading. We will take a random sample of 250 American adults and ask them the question. Then the sampling distribution of the sample proportion of people who answer yes to the question is:

approximately Normal, with mean 0.6 and standard error 0.031.

Suppose 60% of American adults believe Martha Stewart is guilty of obstruction of justice and fraud related to insider trading. We will take a random sample of 100 American adults and ask them the question. Then the sampling distribution of the sample proportion of people who answer yes to the question is:

approximately Normal, with mean 0.6 and standard error 0.04899.

MARK ALL THAT ARE TRUE!! We can use the Normal (Z) table to find probabilities about:

individuals, if the population is Normal averages based on small n, if the population is Normal sample proportion of successes out of n independent trials, when np and n(1-p) is large enough averages based on large n, if the population is Normal averages based on large n, if the population is NOT Normal

Suppose that 75% of adult Americans agree that, while downloading music from the Internet and then selling it is piracy and should be prohibited, downloading for personal use is an innocent act and should not be prohibited.We will take a random sample of 50 American adults and ask them if they agree with the statement. Then the sampling distribution of the sample proportion of people who answer yes to the question is:

neither Normal, not Binomial.

The distribution of the amount of money in savings accounts for Florida State students has an average of 1,200 dollars and a standard deviation of 900 dollars. Suppose that we take a random sample of 10 Florida State students and ask them how much they have in their savings account. The sampling distribution of the sample mean amount of money in a savings account is

not approximately normal

The distribution of the amount of money in savings accounts for Florida State students has an average of 1,200 dollars and a standard deviation of 900 dollars. Suppose that we take a random sample of 100 Florida State students and ask them how much they have in their savings account. The sampling distribution of the sample mean amount of money in a savings account is

not approximately normal

What is the standard error of the sampling distribution of the sample mean?

sqrt(p(1-p)/n)

Go to artofstat.com, click on WebApps and open the Explore Coverage app. Change the tab on top of the graph to Confidence Interval for a Mean. Change the Population Distribution to Bell-shaped and use the default mean=50 and standard deviation=10. Under "Choose confidence level (in %)" use the default 95, and under "Select sample size (n)" use the default of n=20. Under "Select how many samples (of size n) you want to draw from the population" select 10. Click on "Draw sample(s)" and note that ten confidence intervals appear under the population graph. Under Coverage, the app displays two percentages - "cover" and "do not cover". Coverage represents:

the percentage of the 10 intervals that cover the true population mean.