Chapter 2 Study Guide

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.

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.

A convenience sample of 105 statistics students reported the number of texts they sent yesterday, and the results are shown in the following distribution. Which of the following statements is true about this distribution? (the graph is clumped together towards the y-axis and tapers off to the right) a. Because the data set is skewed left, the mean is smaller than the median. b. Because the data set is skewed right, the mean is larger than the median. c. Because the data set is skewed right, the mean is smaller than the median. d. Because the data set is skewed left, the mean is larger than the median.

b/Because the data set is skewed right, the mean is larger than the median.

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

As part of a class project, a student conducts a survey of 50 students at her college finding that, on average, the students in the sample report spending 2.7 hours per day watching TV (SD = 2). The student wonders if this is significantly less then the national average of 3.5 hours per day that college students spend watching TV. The parameter of interest in this study is Select one: a. The sample average hours per day spent watching TV among the 50 students b. The average hours per day spent watching TV among all students at the college c. The average hours per day spent watching TV among all people in the US

b/The average hours per day spent watching TV among all students at the college

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.

As part of a class project, a student conducts a survey of 50 students at her school finding that, on average, the students in the sample report spending 2.7 hours per day watching TV (SD = 2). The student wonders if this is significantly less then the national average of 3.5 hours per day. The t-statistic for this data is found to be -2.83. This means that Select one: a. There is moderate evidence against the null hypothesis b. There is strong evidence against the null hypothesis c. There is little to no evidence against the null hypothesis

b/There is strong evidence against the null hypothesis

sample is

a subset of the population on which we record data

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.

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

In this case, the corresponding parameter of interest can be defined as the ________________ of all students at your school that _________ on the issue.

proportion, agree

If you only interview a subset of the students at your school, this subset is the __________, and the proportion or any number you calculate about this sample would again be considered a _______________

sample, statistic

population of interest

the entire collection of individuals or objects about which information is desired

population is

the entire collection of observational units we are interested in

census

the official count of a population; surveying everyone

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

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]

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.

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

Suppose you are told that the average wingspan of an American robin is 35 cm and you want to test this out for the robins in your area. You capture 40 robins to use as your sample and find that the mean wingspan of your sample is 37 cm. If you were going use your data to test the claim that the average wingspan is not 35 cm, how would you write out the hypotheses in symbols? a. H0: μ = 35 cm, Ha: μ ≠ 35 cm b. H0: μ = 37 cm, Ha: μ ≠ 37 cm c. H0: x̄ = 37 cm, Ha: x̄ ≠ 37 cm d. H0: x̄ = 35 cm, Ha: x̄ ≠ 35 cm

a/H0: μ = 35 cm, Ha: μ ≠ 35 cm

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 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.

Which of the following are the correct validity conditions for a one-sample t-test? a. The quantitative variable should have a symmetric distribution, or you should have at least 20 observations and the sample distribution should not be strongly skewed. b. You should have at least 10 success and at least 10 failures in your sample or a sample size consisting of at least 20 observations. c. You should have at least 10 success and at least 10 failures in your sample. d. The quantitative variable should have a symmetric distribution, or you should have at least 20 observations for any other shape of the sample distribution.

a/The quantitative variable should have a symmetric distribution, or you should have at least 20 observations and the sample distribution should not be strongly skewed.

Is the following statement true or false? The goal of taking a random sample from a population is to end up with a sample which represents (has the characteristics of) the population Select one: a. True b. False

a/True

When assigning symbols to statistics and parameters, which of the following is correct? (Choose all that are correct.) Select one or more: A. x̄ is the sample mean, π is the population mean B. x̄ is the sample mean, μ is the population mean C. p̂ is the sample mean, π is the population mean D. p̂ is the sample proportion, π is the population proportion E. x̄ is the sample proportion, p̂ is the population proportion F. x̄ is the sample proportion, μ is the population proportion G. p̂ is the sample mean, μ is the population mean H. π is the sample proportion, and μ is the population proportion

b and d x̄ is the sample mean, μ is the population mean p̂ is the sample proportion, π is the population proportion

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.

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

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

A sampling method is __________ if statistics from different samples consistently overestimate or consistently underestimate the population parameter of interest. Select one: a. Significant b. Probable c. Biased

c/Biased

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.

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

Which of the following is FALSE? A. We use the symbol x̄ to represent the sample mean. B. The symbols p̂ and x̄ are both used to represent statistics. C. The symbols x̄ and μ are both used to represent statistics. D. We use the symbol μ to represent the population mean.

c/The symbols x̄ and μ are both used to represent statistics.

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

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.

Using simple random sampling allows us to __________________ the results of our study to the entire population. Select one: a. Show causality of b. Does not allow us to do anything c. Summarize d. Generalize

d/Generalize

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

We can reduce the possibility of having bias in a study by: A. Using a one-sided alternative hypothesis instead of a two-sided alternative hypothesis. B. Increasing the sample size. C. Conducting a theory-based test instead of a simulation-based test. D. Making sure our sample is a simple random sample.

d/Making sure our sample is a simple random sample.

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

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.

Which of the following is correct? a. μ and σ represent statistics while x̄ and s represent parameters b. x̄ and μ represent statistics while s and σ represent parameters c. s and σ represent statistics while x̄ and μ represent parameters d. x̄ and s represent statistics while μ and σ represent parameters

d/x̄ and s represent statistics while μ and σ represent parameters

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)

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