Stats Test 1 SG

Suppose a 95% confidence interval for a population proportion is (0.30, 0.60). Rewrite this interval in the form of p̂ ± margin of error . ______ ± ______

0.45,0.15

The spinning dancer (or silhouette illusion) is a moving image of a woman that appears to be spinning. Some people see her spinning clockwise and some see her spinning counterclockwise. A student showed other students this and found that 30 out of 50 (or 60%) of them saw her spinning clockwise. The student researcher was interested in the proportion of people that would see the dancer spinning clockwise. He created the following null distribution for this: Using the information provided above, determine a 2SD 95% confidence interval for the population proportion of people that would see the woman spinning clockwise. (Give all answers to 2 decimal places.) _____ to ______

0.46, 0.74

Recall the previous exercise on cardiac arrests for kidney disease patients. Besides the Monday-Wednesday-Friday schedule for dialysis, many patients are on a Tuesday-Thursday-Saturday schedule. Again, like Monday, Tuesday is unique in that there is the same preceding two-day gap in dialysis. The researchers found that of the 190 cardiac arrests that took place for patients on the Tuesday-Thursday-Saturday schedule, 65 of them occurred on Tuesdays. Do we have convincing evidence of a larger probability of cardiac arrests occurring on Tuesdays compared to the other two days? Investigate by answering the following. H0: HA: Give the value of the statistic. a. p̂ = 0.333 b. π = 0.342 c. π = 0.333 d. p̂ = 0.342 Are the validity conditions met? Explain. a. No, because the number of success (65) and failures (125) are each at least 10. b. Yes, because the sample size is more than 20. c. Yes, because the number of success (65) and failures (125) are each at least 10. d. No, because the sample size is more than 20.

1) H0: π=0.333 HA: π>0.333 2) d/p̂ = 0.342 3) c/Yes, because the number of success (65) and failures (125) are each at least 10.

Patients with kidney disease often have a procedure called dialysis done to clean their blood if their kidneys can't do this properly. This procedure is often done three days per week, with Monday, Wednesday, and Friday often being those days. In terms of the dialysis treatments, these days are all the same except for the gap of two off days before the Monday treatment. Does this gap make a difference? Cardiac arrest and sudden death for patients undergoing dialysis for kidney disease are possibilities. In recent years, it has been noted that these types of patients have cardiac arrests on Mondays more often than what would be expected. A study published in Kidney International (Karnik et al., 2001) looked at 205 dialysis patients that had cardiac arrests on Monday, Wednesday, or Friday, the same days they had dialysis. They found that 93 of these happened on a Monday. Do we have convincing evidence of a larger probability of cardiac arrests occurring on Mondays compared to the other two days? Investigate by answering the following. 1) Use the One Proportion applet to report a simulation-based p-value. Choose the best among the following options a. < 0.001 b. 0.528 c. 0.472 d. 1 2) Use the One Proportion applet to also report a theory-based p-value. a. 0.0001 b. 1 c. 0.0002 d. 0.5000

1) a/< 0.001 2) a/0.0001

Recall the previous exercise on cardiac arrests for kidney disease patients. Besides the Monday-Wednesday-Friday schedule for dialysis, many patients are on a Tuesday-Thursday-Saturday schedule. Again, like Monday, Tuesday is unique in that there is the same preceding two-day gap in dialysis. The researchers found that of the 190 cardiac arrests that took place for patients on the Tuesday-Thursday-Saturday schedule, 65 of them occurred on Tuesdays. Do we have convincing evidence of a larger probability of cardiac arrests occurring on Tuesdays compared to the other two days? Investigate by answering the following. 1) Use the One Proportion applet to report a simulation-based p-value. Choose the best among the following options a. 0.001 b. 1 c. 0.415 d. 0.826 2) Use the One Proportion applet to also report a theory-based p-value. a. 0.7924 b. 0.0014 c. 1 d. 0.3962

1) c/0.415 2) d/0.3962

The applet output shown below has three distributions that involve sampling words from the Gettysburg Address like what was done in Exploration 2.1 when we focused on whether a word was short or not. Choose from the list below each graph that best describes the distribution. the graph's mean is 0.41 the standard deviation 0.096 the graph is bell shaped a. A distribution of proportions of short words taken from many, many random samples b. A distribution of mean word lengths taken from many, many random samples c. A distribution of the proportion of short words (or not) from one sample of size 25 d. A distribution of word lengths from many, many samples e. The population distribution of word lengths f. The population distribution of the proportion of short words (or not)

a/A distribution of proportions of short words taken from many, many random samples

The data did not come from a random sample; rather it came from a convenience sample of healthy adults that were involved in a vaccine study. Given that information, to what population do you think we can generalize our results? Choose the best among the following statements. a. Any generalization should be done with caution, but we can probably generalize it to healthy male adults similar to those that were in the study. b. Any generalization should be done with caution, but we can probably generalize it to all healthy male adults. c. No generalization is allowed because the sample size is small. d. Any generalization should be done with caution, but we can probably generalize it to healthy male adults in the study.

a/Any generalization should be done with caution, but we can probably generalize it to healthy male adults similar to those that were in the study.

Recall the previous exercise on cardiac arrests for kidney disease patients. Besides the Monday-Wednesday-Friday schedule for dialysis, many patients are on a Tuesday-Thursday-Saturday schedule. Again, like Monday, Tuesday is unique in that there is the same preceding two-day gap in dialysis. The researchers found that of the 190 cardiac arrests that took place for patients on the Tuesday-Thursday-Saturday schedule, 65 of them occurred on Tuesdays. Do we have convincing evidence of a larger probability of cardiac arrests occurring on Tuesdays compared to the other two days? Investigate by answering the following. Write out a conclusion in the context of the research question. a. Based on the large p-value, we do not have strong evidence against the null hypothesis. We do not have strong evidence that the long-run proportion of cardiac arrests among dialysis patients that happen on Tuesdays (compared to Thursdays or Saturdays) is greater than 0.333. b. Based on the small p-value, we have strong evidence against the null hypothesis. We have strong evidence that the long-run proportion of cardiac arrests among dialysis patients that happen on Tuesdays (compared to Thursdays or Saturdays) is greater than 0.333. c. Based on the large p-value, we have strong evidence against the null hypothesis. We do not have strong evidence that there is a larger probability of cardiac arrests among dialysis patients occurring on Tuesdays compared to Thursdays or Saturdays. d. Based on the small p-value, we do not have strong evidence against the null hypothesis. We have strong evidence that there is a larger probability of cardiac arrests among dialysis patients occurring on Tuesdays compared to Thursdays or Saturdays.

a/Based on the large p-value, we do not have strong evidence against the null hypothesis. We do not have strong evidence that the long-run proportion of cardiac arrests among dialysis patients that happen on Tuesdays (compared to Thursdays or Saturdays) is greater than 0.333.

Suppose I am conducting a test of significance where the null hypothesis is my dog Bernoulli will pick the correct cancer specimen 25% of the time and the alternative hypothesis is that he will pick the cancer specimen at a rate different than 25%. I end up with a p-value of 0.07. I also construct 95% and 99% confidence intervals from my data. What will be true about my confidence intervals? a. Both the 95% and the 99% intervals will contain 0.25. b. Neither the 95% nor the 99% intervals will contain 0.25. c. The 95% interval will contain 0.25, but the 99% interval will not contain 0.25. d. The 95% interval will not contain 0.25, but the 99% interval will contain 0.25.

a/Both the 95% and the 99% intervals will contain 0.25.

In Example 1.1, we looked at a study to investigate whether dolphins could communicate the idea of left and right. In doing so, we tested whether Buzz, one of the dolphins, understands the communication so would push the correct button more than 50% of the time in the long run. Describe what a Type I error (rejecting a true null hypothesis) would be in this study. a. Buzz does NOT understand the communication so is guessing, but we have strong evidence that he understands the communication b. Buzz understands the communication, but we do NOT have strong evidence that he understands

a/Buzz does NOT understand the communication so is guessing, but we have strong evidence that he understands the communication

In Example 1.1, we looked at a study to investigate whether dolphins could communicate the idea of left and right. In doing so, we tested whether Buzz, one of the dolphins, understands the communication so would push the correct button more than 50% of the time in the long run. Describe what a Type II error (not rejecting a false null hypothesis) would be in this study. a. Buzz understands the communication, but we do NOT have strong evidence that he understands b. Buzz does NOT understand the communication so is guessing, but we have strong evidence that he understands the communication

a/Buzz understands the communication, but we do NOT have strong evidence that he understands

Normal (or average) body temperature of humans is often thought to be 98.6°F. Is that number really the average body temperature for human males? To test this, we will use a data set which consists of 65 body temperatures from healthy male volunteers aged 18 to 40 that were participating in vaccine trials. The data set is also available from the textbook website and is names MaleTemps. What are the appropriate null and alternative hypotheses for this study? a. H0: The average body temperature for males is 98.6°F and Ha: The average body temperature for males is not 98.6°F b. H0: The average body temperature for males is 98.6°F and Ha: The average body temperature for males is greater than 98.6°F c. H0: The average body temperature for males is 98.6°F and Ha: The average body temperature for males is smaller than 98.6°F

a/H0: The average body temperature for males is 98.6°F and Ha: The average body temperature for males is not 98.6°F

Spam filters in an email program are similar to hypothesis tests in that there are two possible decisions and two possible realities and therefore two kinds of errors that can be made. The hypotheses can be considered as: H0: Incoming email message is legitimate. Ha: Incoming email message is spam. Describe what rejecting H0 means in this context. a. Having strong evidence that the incoming email message is spam b. Not having strong evidence that the incoming email message is spam c. Having strong evidence that the incoming email message is legitimate

a/Having strong evidence that the incoming email message is spam

The dotplot below shows the 65 body temperatures. Based on this dotplot, does it appear the average body temperature is different than 98.6°F? Choose the best among the following statements. a. It is hard to tell, because there is a lot of variability in the data. b. Yes, because not all the points are equal to 98.6°F. c. No, because the average of the maximum temperature and the minimum temperature is close to 98.6°F.

a/It is hard to tell, because there is a lot of variability in the data.

The spinning dancer (or silhouette illusion) is a moving image of a woman that appears to be spinning. Some people see her spinning clockwise and some see her spinning counterclockwise. A student showed other students this and found that 30 out of 50 (or 60%) of them saw her spinning clockwise. The student researcher was interested in the proportion of people that would see the dancer spinning clockwise. He created the following null distribution for this: mean: 0.503 Standard Deviation: 0.070 Based on your confidence interval from part (a) do you have strong evidence that the population proportion of people that will see the woman spinning clockwise is greater than 50%? a. No because the confidence interval contains 0.50 b. Yes because the confidence interval is entirely above 0.50

a/No because the confidence interval contains 0.50

The reason for taking a random sample instead of a convenience sample is: Select one: a. Random samples tend to represent the population of interest. b. Random samples tend to be easier to implement and be successful. c. Random samples tend to be smaller and so take less time to collect. d. Random samples always have 100% participation rates.

a/Random samples tend to represent the population of interest.

The Gettysburg Address has 268 words and the average word length is 4.29 letters. If we are going to randomly choose words from that speech, which of the following is least likely to happen? a. Randomly picking 10 words from the Gettysburg Address and have the mean be 2 or fewer letters in length. b. Randomly picking 5 words from the Gettysburg Address and have the mean be 2 or fewer letters in length. c. Randomly picking a word from the Gettysburg Address and have it be 2 or fewer letters in length.

a/Randomly picking 10 words from the Gettysburg Address and have the mean be 2 or fewer letters in length.

If you are testing the hypotheses H0: π = 0.50 and Ha: π ≠ 0.50, have a sample proportion of 0.60 and get a p-value of 0.321, what can you say about a 95% confidence interval constructed using the same data? a. The 95% confidence interval will definitely contain 0.50. b. The 95% confidence interval will definitely not contain 0.60. c. The 95% confidence interval will definitely not contain 0.50. d. The 95% confidence interval will definitely contain 0.321. e. The 95% confidence interval will definitely not contain 0.321.

a/The 95% confidence interval will definitely contain 0.50.

Suppose I am conducting a test of significance where the null hypothesis is my dog Bernoulli will pick the correct cancer specimen 25% of the time and the alternative hypothesis is that she will pick the cancer specimen at a rate different than 25%. I end up with a p-value of 0.02. I also construct 95% and 99% confidence intervals from my data. What will be true about my confidence intervals? a. The 95% interval will not contain 0.25, but the 99% interval will contain 0.25. b. The 95% interval will contain 0.25, but the 99% interval will not contain 0.25. c. Both the 95% and the 99% intervals will contain 0.25. d. Neither the 95% nor the 99% intervals will contain 0.25.

a/The 95% interval will not contain 0.25, but the 99% interval will contain 0.25.

Spam filters in an email program are similar to hypothesis tests in that there are two possible decisions and two possible realities and therefore two kinds of errors that can be made. The hypotheses can be considered as: H0: Incoming email message is legitimate. Ha: Incoming email message is spam. Describe what rejecting a true null hypothesis means in this context. (This is also known as a Type I error.) a. The message is legitimate, but you have strong evidence that the message is spam. b. The message is spam, but you do not have strong evidence that the message is spam. c. The message is spam, but you have strong evidence that the message is legitimate.

a/The message is legitimate, but you have strong evidence that the message is spam.

Suppose a friend of yours says she is a 75% free-throw shooter in basketball. You don't think she is that good and want to test her to gather evidence that she makes less than 75% of her free throws in the long run. You have her shoot 30 free throws and she makes 18 (or 60%) of them. Are the validity conditions met for the one-proportion z-test? Select one: A.Yes, because the number of success and failures are each at least 10. B.No, because the sample size is less than 40. C.No, because the number of success and failures are each at least 10. D.Yes, because the sample size is more than 20.

a/Yes, because the number of success and failures are each at least 10.

Student researchers were interested in whether people will be more likely to choose the name-brand cookie (Chips Ahoy) over the store-brand (Chipsters) in a blind taste test. They tested this with 20 subjects and found that 14 (70%) chose Chips Ahoy as their favorite. They conducted a test of significance using simulation and got the following null distribution. (Note that this null distribution uses only 100 simulated samples and not the usual 1,000 or 10,000.) We will let π represent the long-run proportion of students that pick Chips Ahoy as their favorite. Using the null distribution above, what is the p-value when testing the hypotheses in part (c)? a. p-value = 8/100 = 0.08 b. p-value = 2/100 = 0.02 c. p-value = 6/100 = 0.06 d. p-value = 100/100 = 1

a/p-value = 8/100 = 0.08

Which confidence level would give the narrowest interval? a. 95% b. 85% c. 99% d. 90%

b/85%

A confidence interval is constructed for the population mean hours studied. Which confidence level would give the widest interval? a. 85% b. 99% c. 95% d. 90%

b/99%

The applet output shown below has three distributions that involve sampling words from the Gettysburg Address like what was done in Exploration 2.2 when we focused on the length of the words. Choose from the list to describe each distribution. mean: 4.295 SD: 2.119 a. A distribution of proportions of short words taken from many, many random samples b. A distribution of mean word lengths taken from many, many random samples c. A distribution of word lengths from one sample of 20 words d. A distribution of word lengths from many, many samples The population distribution of word lengths e. A distribution of the proportion of short words (or not) from one sample of size 25

b/A distribution of mean word lengths taken from many, many random samples

Suppose that birth weights of babies in the U.S. have a mean of 3,250 grams and standard deviation of 550 grams. Based on this information, which of the following is more unlikely? Choose one. a. A randomly selected baby has a birth weight greater than 4,000 grams. b. A random sample of 10 babies has an average birth weight greater than 4,000 grams. c. Both are equally likely. d. Cannot be answered without doing calculations.

b/A random sample of 10 babies has an average birth weight greater than 4,000 grams.

Suppose we have a collection of the heights of all students at your school. Also suppose 100 random samples of size 40 are taken from these heights and from each of these samples a 95% confidence interval for the mean height of all students at your school is constructed. Which of these statements about the 100 confidence intervals is most accurate? a. About 95% of the time, the sample mean height will be contained in its corresponding interval. b. About 95% of the intervals will contain the population mean height. c. About 95% of the intervals will be identical. d. About 95% of the heights of all students at the college will be contained in these intervals.

b/About 95% of the intervals will contain the population mean height.

Based on a 2018 General Social Survey poll of 2,347 adult U.S. residents, a 95% confidence interval for the proportion of all U.S. adult residents that were born in the United States is 0.858 to 0.885. Based on these results, which of the following can we make? a. The proportion of all U.S. adults that were born in the United States is definitely between 0.858 and 0.885. b. If they repeated this process (randomly sampling 2,347 U.S. adult residents and finding the proportion of these that were born in the United States) were repeated many, many times, about 95% of the resulting confidence intervals would contain the population proportion of all U.S residents that were born in the United States. c. We are 95% confident that the sample proportion of those that responded to the survey that were born in the United States is between 0.858 and 0.885. d. The methods used in this poll will result in getting 95% of all sample proportions between 0.858 and 0.885

b/If they repeated this process (randomly sampling 2,347 U.S. adult residents and finding the proportion of these that were born in the United States) were repeated many, many times, about 95% of the resulting confidence intervals would contain the population proportion of all U.S residents that were born in the United States

Spam filters in an email program are similar to hypothesis tests in that there are two possible decisions and two possible realities and therefore two kinds of errors that can be made. The hypotheses can be considered as: H0: Incoming email message is legitimate. Ha: Incoming email message is spam. Describe what failing to reject H0 means in this context. a. Having strong evidence that the incoming email message is spam b. Not having strong evidence that the incoming email message is spam c. Having strong evidence that the incoming email message is legitimate

b/Not having strong evidence that the incoming email message is spam

If you are testing the hypotheses H0: π = 0.60 and Ha: π ≠ 0.60, have a sample proportion of 0.75 and get a p-value of 0.021, what can you say about a 99% confidence interval constructed using the same data? a. The 99% confidence interval will definitely not contain 0.75. b. The 99% confidence interval will definitely contain 0.60. c. The 99% confidence interval will definitely contain 0.021. d. The 99% confidence interval will definitely not contain 0.60. None of the above.

b/The 99% confidence interval will definitely contain 0.60.

Let π denote some population proportion of interest and suppose a 95% confidence interval for π is calculated to be (0.63, 0.73) and a 99% confidence interval for π is calculated to be (0.61, 0.75). Also, suppose that we want to test H0: π = 0.74 vs. Ha: π ≠ 0.74 What can you say about the corresponding p-value? a. The corresponding p-value will be larger than 0.05. b. The corresponding p-value will be smaller than 0.05 but larger than 0.01. c. The corresponding p-value will be smaller than 0.01. d. I can't say anything about the corresponding p-value until I run the test.

b/The corresponding p-value will be smaller than 0.05 but larger than 0.01.

A study done in the Netherlands (Stulp et al., 2015) looked to see whether a person's height is related to their status. To test this they found a narrow passage at the entrance of a supermarket where only one person could fit through at a time. They then watched what would happen when two people (of the same sex) approached the passage at the same time, but from opposite ends. Would the shorter person give way to the taller? In the 46 pairs of individuals that they observed, 31 times the shorter person gave way and let the taller pass through first. In the other 15 times, the shorter person was allowed to pass through first. Describe the parameter, π, that the researchers are trying to estimate. a. 23/46 = 0.50 of the time the taller person will pass through first in a same-sex pair of individuals. b. The long-run proportion of times when the taller person will pass through first in a same-sex pair of individuals. c. The proportion of times when the taller person will pass through first in a same-sex pair of individuals in the sample. d. 31/46 = 0.67 of the time the taller person will pass through first in a same-sex pair of individuals.

b/The long-run proportion of times when the taller person will pass through first in a same-sex pair of individuals.

Spam filters in an email program are similar to hypothesis tests in that there are two possible decisions and two possible realities and therefore two kinds of errors that can be made. The hypotheses can be considered as: H0: Incoming email message is legitimate. Ha: Incoming email message is spam. Describe what failing to reject a false null hypothesis error means in this context. (This is also known as a Type II error.) a. The message is legitimate, but you have strong evidence that the message is spam. b. The message is spam, but you do not have strong evidence that the message is spam. c. The message is spam, but you have strong evidence that the message is legitimate.

b/The message is spam, but you do not have strong evidence that the message is spam.

A 95% confidence interval is computed to estimate the mean household income for a city. Which of these values will definitely be within the limits of this confidence interval? a. The p-value b. The sample mean c. The population mean d. The sample standard deviation

b/The sample mean

Suppose you are using theory-based techniques (e.g., a one-proportion z-test) to determine p-values. How will a two-sided p-value compare to a one-sided p-value (assuming the one-sided p-value is less than 0.50)? Select one: A.The two-sided p-value will be close to twice as large as the one-sided. B.The two-sided p-value will be exactly twice as large as the one-sided. C.The two-sided p-value will be about the same as the one-sided. D.The two-sided p-value will be half as much as the one-sided.

b/The two-sided p-value will be exactly twice as large as the one-sided.

Patients with kidney disease often have a procedure called dialysis done to clean their blood if their kidneys can't do this properly. This procedure is often done three days per week, with Monday, Wednesday, and Friday often being those days. In terms of the dialysis treatments, these days are all the same except for the gap of two off days before the Monday treatment. Does this gap make a difference? Cardiac arrest and sudden death for patients undergoing dialysis for kidney disease are possibilities. In recent years, it has been noted that these types of patients have cardiac arrests on Mondays more often than what would be expected. A study published in Kidney International (Karnik et al., 2001) looked at 205 dialysis patients that had cardiac arrests on Monday, Wednesday, or Friday, the same days they had dialysis. They found that 93 of these happened on a Monday. Do we have convincing evidence of a larger probability of cardiac arrests occurring on Mondays compared to the other two days? Investigate by answering the following. Write out a conclusion in the context of the research question. a. Based on the large p-value, we have strong evidence against the null hypothesis. We do not have strong evidence that there is a larger probability of cardiac arrests among dialysis patients occurring on Mondays compared to Wednesdays or Fridays. b. Based on the small p-value, we do not have strong evidence against the null hypothesis. We have strong evidence that there is a larger probability of cardiac arrests among dialysis patients occurring on Mondays compared to Wednesdays or Fridays. c. Based on the small p-value, we have strong evidence against the null hypothesis. We have strong evidence that the long-run proportion of cardiac arrests among dialysis patients that happen on Mondays (compared to Wednesdays or Fridays) is greater than 0.333. d. Based on the large p-value, we do not have strong evidence against the null hypothesis. We do not have strong evidence that the long-run proportion of cardiac arrests among dialysis patients that happen on Mondays (compared to Wednesdays or Fridays) is greater than 0.333.

c/Based on the small p-value, we have strong evidence against the null hypothesis. We have strong evidence that the long-run proportion of cardiac arrests among dialysis patients that happen on Mondays (compared to Wednesdays or Fridays) is greater than 0.333.

The two distributions below are the mean length of words from samples of 10 words and 30 words from the Gettysburg Address. Which distribution comes from samples of size 10 and which from 30? Choose the best among the following statements. a. There is not enough information to answer. b. Graph (a) is a distribution of sample means from samples of size 10; we know this because it is the distribution with the mean closer to the population mean. c. Graph (a) is a distribution of sample means from samples of size 30; we know this because it is the distribution with the smaller standard deviation. d. Graph (a) is a distribution of sample means from samples of size 30; we know this because it is the distribution with the mean closer to the population mean. e. Graph (a) is a distribution of sample means from samples of size 10; we know this because it is the distribution with the smaller standard deviation.

c/Graph (a) is a distribution of sample means from samples of size 30; we know this because it is the distribution with the smaller standard deviation.

The Gettysburg address has 268 words and 41.0% of the words are short (3 or fewer letters). If we are going to randomly choose words from that speech, which of the following is least likely to happen? Select one: a. Randomly picking 5 words from the Gettysburg Address and have all of them be short. b. Randomly picking a word from the Gettysburg Address and have it be short. c. Randomly picking 10 words from the Gettysburg Address and have all of them be short.

c/Randomly picking 10 words from the Gettysburg Address and have all of them be short.

The dotplot below shows the 65 body temperatures. Based on this dotplot, does it appear the average body temperature is different than 98.6°F? Choose the best among the following statements. T-stat: -2.24 p-value: 0.0289 Choose the best conclusion based on the p-value. a. Since the p-value is less than 0.05 we have strong evidence that the average body temperature for females is greater than 98.6 degrees. b. Since the p-value is less than 0.05 we have strong evidence that the average body temperature for females is less than 98.6 degrees. c. Since the p-value is less than 0.05 we have strong evidence that the average body temperature for females is different than 98.6 degrees. d. Since the p-value is less than 0.05 we have strong evidence that the average body temperature for females is equal to 98.6 degrees.

c/Since the p-value is less than 0.05 we have strong evidence that the average body temperature for females is different than 98.6 degrees.

The theorem that states that if the sample size is large enough, the distribution of sample proportions will be bell-shaped (approximately normal), centered at the long run proportion π, with a standard deviation of is called: √(π(1-π)/n) Select one: A. The theory-based theorem. B. The normal theorem. C. The central limit theorem. D. The fundamental theorem of statistics.

c/The central limit theorem.

Let π denote some population proportion of interest and suppose a 95% confidence interval for π is calculated to be (0.60, 0.70). Also, suppose that we want to test H0 : π = 0.63 vs. Ha : π ≠ 0.63. What can you say about the corresponding p-value? a. The corresponding p-value will be smaller than 0.05. b. Need more information to answer this. c. The corresponding p-value will be larger than 0.05.

c/The corresponding p-value will be larger than 0.05

Suppose the distribution of the length of the words in a chapter of your textbook has a mean of 5 words and a standard deviation 2.7 words. Also suppose I take repeated samples of 10 words from all the words in the chapter, calculate the mean of each sample, and repeat this 1,000 times. What will be true about the resulting distribution of sample mean word lengths? a. Since this samples were randomly taken, we have no way to predict the values of the resulting mean and standard deviation. b. The distribution will have a mean of about 5 words and a standard deviation of about 2.7 words. c. The distribution will have a mean of about 5 words and a standard deviation less than 2.7 words. d. The distribution will have a mean of about 5 words and a standard deviation greater than 2.7 words.

c/The distribution will have a mean of about 5 words and a standard deviation less than 2.7 words.

The more left skewed a distribution is a. The smaller the percentage of data values that are above the mean b. The closer the mean and median are together c. The larger the percentage of data values that are above the mean d. The percentage of data values above the mean is roughly the same as the percentage of data values below the mean

c/The larger the percentage of data values that are above the mean

In a 2017 study done with Lee University students, 15 out of 129 respondents said they would rather break a bone than lose their phone. We will assume this comes from a random sample of students at Lee University. Describe the parameter, π, that this poll is trying to estimate. a. The proportion of 129 Lee University students who would rather break a bone than lose their phone. b. 15/129 = 0.116 of all Lee University students who would rather break a bone than lose their phone. c. The proportion of all Lee University students who would rather break a bone than lose their phone.

c/The proportion of all Lee University students who would rather break a bone than lose their phone.

Twenty-nine college students were asked how many states in the U.S. they have been to and the results are shown below. 1, 3, 3, 5, 6, 8, 9, 10, 11, 12, 12, 12, 13, 13, 14, 15, 16, 16, 19, 21, 23, 23, 25, 25, 27, 28, 30, 30, 30 Suppose one of the 30s in the data set was changed to 40. Which of the following statistics would NOT change? a. standard deviation b. The mean, median, and standard deviation would all change c. median d. mean

c/median

Student researchers were interested in whether people will be more likely to choose the name-brand cookie (Chips Ahoy) over the store-brand (Chipsters) in a blind taste test. They tested this with 20 subjects and found that 14 (70%) chose Chips Ahoy as their favorite. They conducted a test of significance using simulation and got the following null distribution. (Note that this null distribution uses only 100 simulated samples and not the usual 1,000 or 10,000.) We will let π represent the long-run proportion of students that pick Chips Ahoy as their favorite. Using the null distribution above, what is the p-value when testing the hypotheses in part (a)? a. p-value = 59/100 = 0.59 b. p-value = 97/100 = 0.97 c. p-value = 3/100 = 0.03 d. p-value = 2/100 = 0.02

c/p-value = 3/100 = 0.03

Suppose a 95% confidence interval for a population proportion is found using the 2SD or theory-based method. Which of the following will definitely be contained in that interval? a. The p-value b. The population proportion c. The sample proportion d. All of the answers shown will be contained in the interval

c/the sample proportion

Suppose you have a large bucket containing 40% red gummy bears and 60% green gummy bears. You take many, many random samples of 25 gummy bears and each time note the proportion that are red. From this, you create a distribution of all your sample proportions of red gummy bears. You should expect the standard deviation of your distribution of sample proportions to be approximately which of the following? Select one: a. 0.400 b. 0.020 c. 0.010 d. 0.098

d/0.098

2.1.3 Suppose you have a large bucket containing 40% red gummy bears and 60% green gummy bears. You take many, many random samples of 25 gummy bears and each time note the proportion that are red. From this, you create a distribution of all your sample proportions of red gummy bears. You should expect the mean of your distribution of sample proportions to be approximately which of the following? Select one: a. 10 b. 0.60 c. 0.50 d. 0.40

d/0.40

For two years, one of the authors asked his students how long they slept the previous night. He now has 255 results with a mean of 7.12 hours and a standard deviation of 1.59 hours. This distribution of sleep times is fairly symmetric. We will call these 255 sleep times a population and then take many, many random samples of 10 sleep times from this population. From this, we create a distribution of the sample means from all the resulting samples. We should expect the standard deviation of this distribution of sample means to be approximately which of the following? a. 1.59 b. 7.12 c. 0.10 d. 0.50 e. 2.25

d/0.50

The sample mean body temperature for the 65 males in our sample to be 98.105°F and the standard deviation to be 0.699°F. Use these summary statistics and the Theory-Based Inference applet to find and report a standardized statistic (t-statistic) and a p-value for the test. Round answer to 2 decimal places, e.g. 0.29. Choose the best conclusion based on the p-value. a. Because the p-value is less than 0.05 we have strong evidence that the male body temperature is not 98.6°F. b. Because the p-value is less than 0.05 we have strong evidence that the male body temperature is 98.6°F. c. Because the p-value is less than 0.05 we have strong evidence that the average male body temperature is 98.6°F. d. Because the p-value is less than 0.05 we have strong evidence that the average male body temperature is not 98.6°F.

d/Because the p-value is less than 0.05 we have strong evidence that the average male body temperature is not 98.6°F.

Which of the following is NOT true about theory- based confidence intervals for a population proportion? a. The process used to construct the interval relies on a normal distribution. b. They can be calculated using different confidence levels. c. They should only be used when you have at least 10 successes and 10 failures in your sample data. d. For a given sample proportion, sample size, and confidence level, different intervals can be obtained because of their random nature.

d/For a given sample proportion, sample size, and confidence level, different intervals can be obtained because of their random nature.

Normal (or average) body temperature of humans is often thought to be 98.6°F. Is that number really the average body temperature for human females? To test this, we will use a data set which consists of 65 body temperatures from healthy female volunteers aged 18 to 40 that were participating in vaccine trials. The data set FemaleTemps consisting of body temperatures from the 65 females is available from the textbook website. You will use the data to investigate whether the average body temperature of healthy adult females is different from 98.6°F. What are the appropriate null and alternative hypotheses for this study? a. H0: x̄ = 98.6°F and Ha: x̄ < 98.6°F b. H0: x̄ = 98.6°F and Ha: x̄ ≠ 98.6°F c. H0: μ = 98.6°F and Ha: μ < 98.6°F d. H0: μ = 98.6°F and Ha: μ ≠ 98.6°F

d/H0: μ = 98.6°F and Ha: μ ≠ 98.6°F

A one-sample t-test gives more valid p-values with: a. Any sample size with any shaped sample distributions b. Smaller sample sizes and sample distributions that are fairly skewed c. Smaller sample sizes and sample distributions that are fairly bell-shaped d. Larger sample sizes and sample distributions that are fairly bell-shaped e. Larger sample sizes and sample distributions that are fairly skewed

d/Larger sample sizes and sample distributions that are fairly bell-shaped

Suppose 10 coins are flipped, and the proportion of heads is recorded. This process is repeated many, many times to develop a distribution of these sample proportions. What is the predicted mean and standard deviation for this distribution of sample proportions? Select one: A. Mean = 0.500, SD = 1.581 B. Mean = 5.000, SD = 1.581 C. Mean = 5.000, SD = 0.581 D. Mean = 0.500, SD = 0.158

d/Mean = 0.500, SD = 0.158

Suppose I am conducting a test of significance where the null hypothesis is my dog Bernoulli will pick the correct cancer specimen 25% of the time and the alternative hypothesis is that she will pick the cancer specimen at a rate different than 25%. I end up with a p-value of 0.002. I also construct 95% and 99% confidence intervals from my data. What will be true about my confidence intervals? a. The 95% interval will not contain 0.25, but the 99% interval will contain 0.25. b. Both the 95% and the 99% intervals will contain 0.25. c. The 95% interval will contain 0.25, but the 99% interval will not contain 0.25. d. Neither the 95% nor the 99% intervals will contain 0.25.

d/Neither the 95% nor the 99% intervals will contain 0.25.

Let π denote some population proportion of interest and suppose a 99% confidence interval for π is calculated to be (0.60, 0.70). Also, suppose that we want to test H0: π = 0.74 vs. Ha : π ≠ 0.74 What can you say about the corresponding p-value? a. The corresponding p-value will be larger than 0.05. b. I can't say anything about the corresponding p-value until I run the test. c. The corresponding p-value will be smaller than 0.05 but larger than 0.01. d. The corresponding p-value will be smaller than 0.01.

d/The corresponding p-value will be smaller than 0.01.

The applet output shown below has three distributions that involve sampling words from the Gettysburg Address like what was done in Exploration 2.2 when we focused on the length of the words. Choose from the list to describe each distribution. mean: 4.295 SD: 2.119 a. A distribution of proportions of short words taken from many, many random samples b. A distribution of mean word lengths taken from many, many random samples c. A distribution of word lengths from one sample of 20 words d. A distribution of word lengths from many, many samples The population distribution of word lengths e. A distribution of the proportion of short words (or not) from one sample of size 25

d/The population distribution of word lengths

Based on a June 2019 Gallup poll, a 95% confidence interval for the proportion of American adults that think a college education is very important is 0.50 to 0.56. Explain exactly what the confidence interval is estimating. a. Whether 0.50 to 0.56 of American adults think a college education is very important. b. The number of American adults in the sample that think a college education is very important. c. The proportion of American adults in the poll that think a college education is very important. d. The proportion of all American adults that think a college education is very important.

d/The proportion of all American adults that think a college education is very important.

In Exploration 2.1, you used an applet to take many samples of words from the Gettysburg Address, found the proportion of short words in each sample, and then created a distribution of the sample proportions. To reduce the standard deviation of the distribution of sample proportions, you could have: Select one: a. Used a smaller sample size. b. Take more samples. c. Take fewer samples. d. Used a larger sample size.

d/Used a larger sample size.

If the sample size were 1,500 instead of 150, the width of a 95% confidence interval would

decrease

If the standard deviation were 0.78 hours instead of 1.05, the width of a 95% confidence interval would decrease or increase

decrease

Suppose we have a list of all 3,000 students in your college and we randomly choose 30 from that list. Each of these 30 people is sent a survey and 25 are returned. In this scenario, what is the sampling frame? Select one: a. The survey b. The mechanism used to randomly choose the 30 students c. The 25 people that returned the survey d. The 30 people sent the survey e. The list of all 3,000 people in your college

e/The list of all 3,000 people in your college

The applet output shown below has three distributions that involve sampling words from the Gettysburg Address like what was done in Exploration 2.1 when we focused on whether a word was short or not. Choose from the list below each graph that best describes the distribution. The graph has more "no" answers Proportion for "yes": 0.410 a. A distribution of proportions of short words taken from many, many random samples b. A distribution of mean word lengths taken from many, many random samples c. A distribution of the proportion of short words (or not) from one sample of size 25 d. A distribution of word lengths from many, many samples e. The population distribution of word lengths f. The population distribution of the proportion of short words (or not)

f/The population distribution of the proportion of short words (or not)

If the sample size were 15 instead of 150, the width of a 95% confidence interval would

increase

If the standard deviation were 1.25 hours instead of 1.05, the width of a 95% confidence interval would decrease or increase

increase

In Example 1.4 we looked to see whether the competent-face method could be used to predict the results of Senate races. We found this method worked in 23 out of 32 races. When testing to see if the probability of this method working is more than 0.50, we obtained a null distribution similar to that shown. Should a theory-based approach be used to compute the confidence interval for these data?

no because there is not at least 10 success nor 10 failures

The sample mean body temperature for the 65 males in our sample to be 98.105°F and the standard deviation to be 0.699°F. Use these summary statistics and the Theory-Based Inference applet to find and report a standardized statistic (t-statistic) and a p-value for the test. Round answer to 2 decimal places, e.g. 0.29. t-statistic = p-value =

t stat: -5.71 p-value: 0

A t-distribution is shaped like a normal distribution but is: a. A bit more spread out and more observations in the tails than a normal distribution. b. A bit taller in the middle than a normal distribution. c. A bit skewed in one direction or the other. d. Not quite as spread out with fewer observations in the tails than a normal distribution.

a/A bit more spread out and more observations in the tails than a normal distribution.

Patients with kidney disease often have a procedure called dialysis done to clean their blood if their kidneys can't do this properly. This procedure is often done three days per week, with Monday, Wednesday, and Friday often being those days. In terms of the dialysis treatments, these days are all the same except for the gap of two off days before the Monday treatment. Does this gap make a difference? Cardiac arrest and sudden death for patients undergoing dialysis for kidney disease are possibilities. In recent years, it has been noted that these types of patients have cardiac arrests on Mondays more often than what would be expected. A study published in Kidney International (Karnik et al., 2001) looked at 205 dialysis patients that had cardiac arrests on Monday, Wednesday, or Friday, the same days they had dialysis. They found that 93 of these happened on a Monday. Do we have convincing evidence of a larger probability of cardiac arrests occurring on Mondays compared to the other two days? Investigate by answering the following. 1) Give the value of the statistic. a. p̂ = 0.500 b. p̂ = 0.454 c. π = 0.500 d. π = 0.454 2) Are the validity conditions met? Explain. a. Yes, because the number of success (112) and failures (93) are each at least 10. b. No, because the number of success (112) and failures (93) are each at least 10. c. No, because the number of success (93) and failures (112) are each at least 10. d. Yes, because the number of success (93) and failures (112) are each at least 10.

1. b/p̂ = 0.454 2. d/Yes, because the number of success (93) and failures (112) are each at least 10.

If you took repeated samples of size 150 and constructed a 95% confidence interval for the population mean study hours from each sample, what percentage of these intervals would capture the population mean study hours?

95%

If you took repeated samples of size 150 and constructed a 99% confidence interval for the population mean of study hours from each sample, what percentage of these intervals would capture the population mean of study hours?

99%

Patients with kidney disease often have a procedure called dialysis done to clean their blood if their kidneys can't do this properly. This procedure is often done three days per week, with Monday, Wednesday, and Friday often being those days. In terms of the dialysis treatments, these days are all the same except for the gap of two off days before the Monday treatment. Does this gap make a difference? Cardiac arrest and sudden death for patients undergoing dialysis for kidney disease are possibilities. In recent years, it has been noted that these types of patients have cardiac arrests on Mondays more often than what would be expected. A study published in Kidney International (Karnik et al., 2001) looked at 205 dialysis patients that had cardiac arrests on Monday, Wednesday, or Friday, the same days they had dialysis. They found that 93 of these happened on a Monday. Do we have convincing evidence of a larger probability of cardiac arrests occurring on Mondays compared to the other two days? Investigate by answering the following. Set up the correct null and alternative hypotheses in symbols. H0: HA+

H0: π=0.333 HA: π>0.333

Student researchers were interested in whether people will be more likely to choose the name-brand cookie (Chips Ahoy) over the store-brand (Chipsters) in a blind taste test. They tested this with 20 subjects and found that 14 (70%) chose Chips Ahoy as their favorite. They conducted a test of significance using simulation and got the following null distribution. (Note that this null distribution uses only 100 simulated samples and not the usual 1,000 or 10,000.) We will let π represent the long-run proportion of students that pick Chips Ahoy as their favorite. a. Set up the correct the null and alternative hypotheses in symbols for the research question, "Do a majority of students prefer Chips Ahoy over Chipsters?" H0= HA=

H0: π=0.5 HA: π>0.5

Student researchers were interested in whether people will be more likely to choose the name-brand cookie (Chips Ahoy) over the store-brand (Chipsters) in a blind taste test. They tested this with 20 subjects and found that 14 (70%) chose Chips Ahoy as their favorite. They conducted a test of significance using simulation and got the following null distribution. (Note that this null distribution uses only 100 simulated samples and not the usual 1,000 or 10,000.) We will let π represent the long-run proportion of students that pick Chips Ahoy as their favorite. Set up the correct the null and alternative hypotheses in symbols for the research question, "Do students have a preference between Chips Ahoy and Chipsters?" H0: HA:

H0: π=0.50 HA: π ≠ 0.50

Based on a 2018 General Social Survey poll, a 95% confidence interval for the proportion of all U.S. adults that were born in the United States is 0.8580 to 0.8850. (a) What proportion of the sample responded that they were born in the United States? (Round answer to 4 decimal places, e.g. 0.1234) Sample proportion = _______ (b) What is the margin of error for the confidence interval? (Round answer to 4 decimal places, e.g. 0.1234) Margin of error = _________

Sample proportion: 0.8715 Margin of Error: 0.0135

The dotplot below shows the 65 body temperatures. Based on this dotplot, does it appear the average body temperature is different than 98.6°F? Choose the best among the following statements. Use the Theory-Based Inference applet to find and report a standardized statistic (t-statistic) and a p-value for the test. Report answers as provided in the applet (no rounding). t- statistic: p-value:

T-stat: -2.24 p-value: 0.0289

Suppose a recent Gallup poll showed the president's approval rating at 60%. Some friends use this information (along with the sample size from the poll) and find theory-based confidence intervals for the proportion of all adult Americans that approve of the presidents performance. Of the following four confidence intervals, identify the ones that were definitely done incorrectly. (There may be more than one interval that is incorrect.) Select one or more: a. (0.47, 0.53) b. (0.57, 0.63) c. (0.60, 0.66) d. (0.58, 0.62)

a and c/(0.47, 0.53) and (0.60, 0.66)

What do you expect the means and standard deviations of the distribution of sample proportions to be for the following population parameters and sample sizes? Round answer to 3 decimal places, e.g. 0.237. a. π = 0.25, n = 40 Mean: SD: b. π = 0.25, n = 400. Mean: SD:

a. Mean: 0.25; SD: 0.068 b. Mean: 0.25; SD: 0.022 SD: √[mean (1-mean)/ n]

Suppose you are testing the hypotheses H0: π = 0.50 versus Ha: π > 0.50. You get a sample proportion of 0.68 and find that your p-value is 0.02. Now suppose you redid your study with each of the following changes, will your new p-value be larger, smaller, or stay the same as the 0.02 you first obtained? Be sure to explain your reasoning. a. Keeping the sample size the same, you take a new sample and find a sample proportion of 0.66. The new p-value will be *larger or smaller* because *option 1, 2, or 3* b. You increase the sample size and still find a sample proportion of 0.68. The new p-value will be *larger or smaller* because *option 1, 2, or 3* c. You decide to use a two-sided alternative hypothesis (Ha: π ≠ 0.50). The new p-value will be *larger or smaller* because *option 1, 2, or 3* Option 1: the p-value calculation now includes at least as extreme values of the statistic in both tails of the null distribution Option 2: the sample proportion is closer to the hypothesized long-run proportion value of 0.5 Option 3: it is less likely to get extreme value of the statistic from a larger sample

a. larger, option 2 b. smaller, option 3 c. larger, option 1

Suppose you are testing the hypotheses H0: π = 0.50 versus Ha: π > 0.50. You get a sample proportion of 0.68 and find that your standardized statistic is 2.53. Now suppose you redid your study with each of the following changes; will your new standardized statistic be larger, smaller, or stay the same as the 2.53 you first obtained? Explain your reasoning. a. Keeping the sample size the same, you take a new sample and find a sample proportion of 0.66. The new standardized statistic will be *smaller (closer to 0) 0r the same or larger (farther from 0)* because *option 1, 2, or 3* b. You increase the sample size and still find a sample proportion of 0.68. The new standardized statistic will be *smaller (closer to 0) 0r the same or larger (farther from 0)* because *option 1, 2, or 3* c. You decide to use a two-sided alternative hypothesis (Ha: π ≠ 0.50). The new standardized statistic will be *smaller (closer to 0) 0r the same or larger (farther from 0)* because *option 1, 2, or 3* Option 1: the sample proportion os closer to the hypothesizes long run proportion value of 0.50 Option 2: it is less likely to get extreme values of the statistic from a larger sample Option 3: the sample proportion is still the same distance away from the center of the null distribution

a. smaller (closer to 0), option 1 b. larger (farther from 0), option 2 c. the same, option 3

In a 2017 study done with Lee University students, 15 out of 129 respondents said they would rather break a bone than lose their phone. We will assume this comes from a random sample of students at Lee University. (b) Use the One Proportion applet, repeatedly testing possible values for π, to construct a 95% confidence interval for π to 2 decimal places. Which of the following is closest to the confidence interval you obtained? a. (0.07, 0.18) b. (0.00, 15.00) c. (0.03, 0.20) d. (15.00, 129.00)

a/(0.07, 0.18)

Which sample size, n, gives the smallest standard deviation of the null distribution where the long-run proportion, π, is 0.25? Select one: A. 60 B. 30 C. 50 D. 40

a/60

When surveys are administered, it is hoped that the respondents give accurate answers. Does the mode of survey delivery affect this? American researchers investigated this question (Schober et al., 2015). They had 634 people agree to be interviewed on an iPhone and they were randomly assigned to receive a text message or a phone call. One question that was asked was whether they exercise less than once per week on a typical week (an example of a question in which an answer of "yes" would be considered socially undesirable). They found that 25.4% of those that received text messages responded yes, while only 13.2% of those that received phone calls responded yes. This difference is statistically significant, and one could assume that one method of the delivery of the question is biased. Which of these results do you think are the result of a biased method of collecting the data and why? Choose the best among the following statements. Select one: a. Both methods of asking this question are probably biased. It is expected about 50% of participants to answer "yes", but both methods led to values much smaller than 50%. b. Using a phone call as the method of asking this question is probably a biased method. Those answering a person on a phone call were much more unlikely to say that they exercise less than once per week. Having an interaction with a person probably makes some people not give the socially undesirable answer. c. Using the text message as the method of asking this question is probably a biased method. The percentage of participants saying "yes" who received text messages is almost twice the percentage of participants saying "yes" who received a phone call. Text message participants are much more likely to say they exercise less. d. None of the methods of asking this question are biased. The difference could be just due to chance.

b/Using a phone call as the method of asking this question is probably a biased method. Those answering a person on a phone call were much more unlikely to say that they exercise less than once per week. Having an interaction with a person probably makes some people not give the socially undesirable answer.

In Example 1.4 we looked to see whether the competent-face method could be used to predict the results of Senate races. We found this method worked in 23 out of 32 races. When testing to see if the probability of this method working is more than 0.50, we obtained a null distribution similar to that shown. Based on your confidence interval from part (a) is there strong evidence that the probability that the competent-face method will work is greater than 50%? a. No because the confidence interval contains 0.50 b. Yes because the confidence interval is entirely above 0.50

b/Yes because the confidence interval is entirely above 0.50

The more right skewed a distribution is a. The percentage of data values below the mean is roughly the same as the percentage of data values above the mean b. The larger the percentage of data values that are below the mean c. The closer the mean and median are d. The smaller the percentage of data values that are below the mean

b/the larger the percentage of data values that are below the mean

In Example 1.4 we looked to see whether the competent-face method could be used to predict the results of Senate races. We found this method worked in 23 out of 32 races. When testing to see if the probability of this method working is more than 0.50, we obtained a null distribution similar to that shown. mean: 0.501 standard deviation: 0.090 Using the information provided above, determine a 2SD 95% confidence interval for the probability the competent-face method will work. (Give all answers to 2 decimal places.) ____ to ____

blank

A study done in the Netherlands (Stulp et al., 2015) looked to see whether a person's height is related to their status. To test this they found a narrow passage at the entrance of a supermarket where only one person could fit through at a time. They then watched what would happen when two people (of the same sex) approached the passage at the same time, but from opposite ends. Would the shorter person give way to the taller? In the 46 pairs of individuals that they observed, 31 times the shorter person gave way and let the taller pass through first. In the other 15 times, the shorter person was allowed to pass through first. Use the One Proportion applet, repeatedly testing possible values for π, to construct a 90% confidence interval for π to 2 decimal places. Which of the following is closest to the confidence interval you obtained? a. (0.53, 0.79) b. (0.48, 0.82) c. (0.55, 0.78)

c/(0.55, 0.78)

According to the 2019 National Coffee Drinking Study from the National Coffee Association, 63% of 2,815 U.S. adults respondents reported drinking coffee in the past 24 hours. Based on these data, use the Theory-Based Inference applet to find a theory-based 99% confidence interval for the proportion of all adult Americans that drank coffee in the previous 24 hours. a. 0.5930 to 0.6670 b. 0.6120 to 0.6477 c. 0.6064 to 0.6533 d. 0.6149 to 0.6448

c/0.6064 to 0.6533

Suppose a 95% confidence interval is constructed from a sample proportion and 0.50 is contained in the interval. Which of the following is true? a. A 99% confidence interval constructed from the same sample proportion will definitely NOT contain 0.50. b. A 90% confidence interval constructed from the same sample proportion will definitely NOT contain 0.50. c. A 99% confidence interval constructed from the same sample proportion will definitely contain 0.50. d. A 90% confidence interval constructed from the same sample proportion will definitely contain 0.50.

c/A 99% confidence interval constructed from the same sample proportion will definitely contain 0.50.

The applet output shown below has three distributions that involve sampling words from the Gettysburg Address like what was done in Exploration 2.1 when we focused on whether a word was short or not. Choose from the list below each graph that best describes the distribution. The graph has more "no" answers Proportion for "yes": 0.440 (the gap between 0.44 between no and yes a. A distribution of proportions of short words taken from many, many random samples b. A distribution of mean word lengths taken from many, many random samples c. A distribution of the proportion of short words (or not) from one sample of size 25 d. A distribution of word lengths from many, many samples e. The population distribution of word lengths f. The population distribution of the proportion of short words (or not)

c/A distribution of the proportion of short words (or not) from one sample of size 25

The applet output shown below has three distributions that involve sampling words from the Gettysburg Address like what was done in Exploration 2.2 when we focused on the length of the words. Choose from the list to describe each distribution. mean: 4.295 SD: 2.119 a. A distribution of proportions of short words taken from many, many random samples b. A distribution of mean word lengths taken from many, many random samples c. A distribution of word lengths from one sample of 20 words d. A distribution of word lengths from many, many samples The population distribution of word lengths e. A distribution of the proportion of short words (or not) from one sample of size 25

c/A distribution of word lengths from one sample of 20 words