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introduction to statistical investigations

Questions and Answers of Introduction To Statistical Investigations

One of the key ideas in Section 2.2 was that the standard deviation of sample means is estimated by σ/√n? , when the population is large enough. We consider a population to be large enough when
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.,
Suppose you have a sample consisting of the numbers 3, 6, and 9 and you use those numbers to develop a bootstrap sampling distribution. a. There are only 10 combinations of the numbers 3, 6, and
The applet output shown for Exercise 2.1.15 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
Suppose you put your pocket change into a bowl when you come home every day and after a few weeks have a collection of 100 coins. We will assume your coins are representative of all coins in
As part of the General Social Survey (GSS) in 2018, a random sample of U.S. adults were asked whether they have ever been told by a health professional that they have depression. In the sample of
A convenience sample of 105 statistics students reported the number of texts they sent yesterday, and the results are shown in the Exercise 2.4.15 graph. If two more students reported their number of
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 A–C is least likely to happen? A. Randomly
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
An eighth-grade student in Canada was concerned that air dryers in public restrooms were too loud, especially when measured at the height of children’s ears. Her results were eventually published
You may have heard the phrase “Music soothes the savage beast,” which is actually a misquote of a line of poetry by William Congreve. Researchers (Wallace et al., 2017) examined what effect music
The multiplier used for calculating a 95% two-sample z-interval for a difference in population proportions is 1.96. For a similar 90% confidence interval the multiplier: A. Is smaller. B.
What value should you put in the cell with the question mark in the table so that there is no association between group and outcome? A. 30B. 35C. 60D. 70E. 100 Success Failure Total Group
Suppose that in a randomized experiment investigating the effect of incentive on whether a person agrees to take a survey, the data are as given in this table. What is an appropriate way to
True or False? For each question, indicate whether the statement is true or false. If the statement is false, briefly explain why. a. In general, when sample sizes increase, the standard
A survey of 122 statistics students included a question that asked them if they are a regular coffee drinker and if they took a nap in the past 3 days. Use the results shown in this mosaic plot to
In Example 5.1, you looked at data comparing seat belt use from direct observations made by the National Highway Traffic Safety Administration in 2008 and 2018. In the mosaic plot here, we compare
Can we make a cause-and-effect conclusion? Why or why not?Let’s use our 3S strategy to help us investigate how much evidence the sample data provide to support our conjecture that Vitamin C
Suppose you are conducting a test of significance in the following situations. For each of these, determine whether you should conduct a one-proportion z-test or a two-proportion z-test. a. You
Suppose you are conducting a test of significance in the following situations. For each of these, determine whether you should conduct a one-proportion z-test or a two-proportion z-test. a. You
The General Social Survey is conducted every year and asks a variety of questions to a representative sample of non-institutionalized adults in the United States. In 2014, the survey showed that 417
Student researchers were doing a project on obedience by seeing whether students would obey the instructions on a sign placed next to a bowl of candy. The sign read: “Have a great day! Please take
The General Social Survey is conducted every year and asks a variety of questions to a representative sample of non-institutionalized adults in the United States. In 2014, the survey showed that
Are metal bands used for tagging harmful to penguins? Researchers Saraux and colleagues (Nature, 2011) reported the results of a study done to investigate this using a sample of 100 penguins near
In a sample of 50 births, each birth was recorded as either a term birth (gestation period of 32 weeks or more) or a preterm birth (gestation period of less than 32 weeks). Is the proportion of
Student researchers at a private Midwestern college were interested in cell phone usage by students on campus and how it varied during different times of the day. They observed students walking
A random sample of high school students were asked, “What is your favorite season?” Out of 468 students in Florida, 149 said winter, whereas only 76 out of 458 from New York said winter. We want
Are there differences in the efficacy of duct tape versus cryotherapy in the treatment of the common wart (Arch Pediatric & Adolescent Medicine 156: 971–974; Focht et al., 2002). To answer this
In a sample of 50 births, a term birth was recorded as 32 weeks or more of gestation, and a preterm birth as less than 32 weeks. We will use these data to compare the proportion of Caesarean
Research on reducing stuttering in preschool children ages 3 to 6 looked at 199 children who were registered in one of 20 participating speech therapy clinics throughout the Netherlands. The children
Are there differences in the efficacy of duct tape versus cryotherapy in the treatment of the common wart? To answer this question, 61 participants between the ages of 3 to 22 years were randomly
Suppose you are doing a test to see whether there is a significant difference in the average weight of white-breasted nuthatches (W) and red-breasted nuthatches (R). Which of A-E is the correct way
Twenty-nine college students were asked how many states in the United States they have been to and the results are shown below. The lower quartile, median, and upper quartile consist of which of the
Suppose you have a dataset with the following summary statistics: lower quartile = 18, median = 22, upper quartile = 28. Which of the following numbers would be outliers according to the 1.5 × IQR
What is an advantage of a standardized statistic (e.g. t-statistic) over a statistic that is not standardized (e.g. difference in means)? A. It is easier to estimate strength of evidence from a
A two-sample t-test gives more valid p-values with: A. Larger sample sizes and sample distributions that are fairly bell-shaped. B. Larger sample sizes and sample distributions that are
Suppose we are testing two means using a two-sided test and get a p-value of 0.03. We also construct a 95% confidence interval from the same data. We would expect: A. 0.03 to be in the
A theory-based test for comparing two means uses which of A–D to approximate a null distribution? A. A normal distribution B. A t-distribution that is a bit wider (or heavier in the
Researchers at Northwestern University explored whether meditation helps someone become a more compassionate person (Lim et al., 2015). To do this, they recruited 56 university students, all of whom
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
In a March 2018 national poll based on a representative sample of 2,737 adult Americans, 64% reported drinking at least one cup of coffee per day. Now suppose that we test the null hypothesis π =
Reconsider Exercise 3.3.24 about the average number of states all students at the author’s school have visited. Recall that in the author’s sample of 136 students the average number of tates the
In a July 2018 Gallup poll that surveyed 1,033 randomly selected U.S. adults, 5% said that they considered themselves vegetarians. a. Describe what the parameter is in this context. b. The
Suppose a 95% confidence interval for a population proportion is (0.27, 0.49). Rewrite this interval in the form of p? ± margin of error.
Which confidence interval would be the narrowest? A. 99% B. 95% C. 90% D. 85%.In order to investigate how many hours a day students at their school tend to spend on course work
The General Social Survey (GSS), conducted every other year, uses a random sample of U.S. adults to gather data on contemporary American society. One of the questions in the 2018 GSS was, “A doctor
Student researchers wanted to determine a person’s ability to estimate the number of beans in a bag. They had 1,470 beans in a clear bag for the subjects to estimate. They also showed the subjects
Do people think they look different than they actually do? In particular, do they think they look better? Researchers Epley and Whitchurch (2008) tried to answer this question by taking pictures of
With the increased use of credit cards, debit cards, and other electronic methods of payment, will the United States eventually stop using cash? In a July 2016 Gallup poll of a random sample of 1,024
The General Social Survey (GSS) uses a random sample of U.S. adults to answer a variety of questions. From the 2018 survey, one question asked was, “On the average day, about how many hours do you
The General Social Survey (GSS) uses a random sample of U.S. adults to answer a variety of questions. From the 2018 survey, one question asked was the age of the respondent when their first child was
Student researchers wanted to know whether students at their school could accurately estimate the length of a 17-second song snippet on average. They played 17 seconds of Corinne Bailey Rae’s song
A Gallup poll from January 2018 found that only 39% of adult Americans planned on watching a great deal/fair amount of the Winter Olympic Games. This information can be used to estimate the
Suppose we are constructing a confidence interval using repeated tests of significance to develop an interval of plausible values. Using two-sided tests each time with the following null hypothesized
Suppose we are constructing a confidence interval using repeated tests of significance to develop an interval of plausible values. Using two-sided tests each time with the following null
Which confidence interval would be the narrowest? A. 99% B. 95% C. 90% D. 85%In order to understand why consumers visit their store, a local business conducts a survey by asking
Based on a June 2019 Gallup poll, a 95% confidence interval for the proportion of American adults that are in favor of free tuition at a community college for anyone who wants to attend is 0.61 to
An eighth-grade student in Canada was concerned that air dryers in public restrooms were too loud, especially when measured at the height of children’s ears. Her results were eventually published
Reconsider Exercises 3.3.24 and 3.3.25 about the average number of states all students at the author’s school have visited. Recall that in the author’s sample of 136 students the average number
In a June 2019 Reuters poll based on a representative sample of 400 American independent voters, 65% responded they support samesex marriages. Now suppose we test the null hypothesis π = 0.50 vs.
Recall Questions 4.1.1 and 4.1.2 about intrinsic motivation and position in the classroom. Which of these is the response variable? A. The classrooms B. The health science students C.
Recall Question 4.1.1 about intrinsic motivation and position in the classroom. Which of these is the explanatory variable? A. The classrooms B. The health science students C. The
A study done in France (Uffler et al., 2017) explored whether there is an association between a student’s intrinsic motivation and where they sit in class. More specifically, they studied 593
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
A 2019 Ipsos poll of 4,000 U.S. adults found that 65% play video games on their computer, gaming console, or smartphone. a. Use this sample result and a theory-based approach to produce three
Refer to Exercise 3.4.32 to answer (a) and (b): a. If the sample size had been 8,000, how would the widths of the 90%, 95%, and 99% confidence intervals be affected? b. If the sample size
A 2015 Gallop poll of 15,747 U.S. adults who had a smartphone found that 72% checked their phones about once every hour. Based on these data we found the 95% confidence interval for the proportion of
Show that the margin-of-error formula simplifies to approximately 1/√n when p? = 0.5 1.96√p(1-P)/n
A 2018 General Social Survey (GSS) asked a random sample of 1,118 adult Americans how often they contacted their closest friend by either phone, internet, other communication device, or face to face.
Although flipping a coin should result in 50% heads in the long run, what proportion of the time will spinning coins on a table result in landing heads up? Determine this with a coin of your choice,
Founded in 1890, the Literary Digest was a popular magazine in the early 1900s. The magazine correctly predicted the outcomes of the 1916, 1920, 1924, 1928, and 1932 presidential elections by
A group of 11 students were asked how many texts they sent yesterday. Put the results, which are in the file Texts, into the One Mean applet and create a bootstrap sampling distribution. Based on the
What do you expect the means and standard deviations of the distribution of sample proportions to be for these population parameters and sample sizes? a. π = 0.25, n = 40 b. π = 0.25, n =
Scores on a recent statistics exam had a mean of 82.7 and a median of 87. If your score on this exam was an 84, did more students in the class have scores higher than yours or lower than yours?
In the Sampling Words applet with the Gettysburg Address using the variable short, the horizontal axis of the population represents whether or not a word is short—a categorical variable. When you
For each of the statements (a)–(d), indicate whether it is true or false. a. The distribution of the variable height can be skewed to the right. b. The distribution of the variable
One of the key ideas in Section 2.1 is that the standard deviation of a distribution of sample proportions is estimated bywhen the population large enough, where large enough was when the population
In the Sampling Words applet with the Gettysburg Address using the variable length, the numbers on the horizontal axis of the graph for the population distribution represent the length of the
For each of the statements (a)–(d), indicate whether it is true or false. a. The distribution of the variable sex can be skewed to the left. b. The distribution of the variable age can be
Recall Exercise 2.CE.13 about healthy human body temperatures. Suppose you are testing the following hypotheses: H0: μ = 98.6°F, Ha: μ ≠ 98.6°F. You recruit 30 healthy subjects and find their
State the appropriate null and alternative hypotheses to be tested. Of the 1,858 cell phone users, 13% admitted to faking cell phone calls in the past 30 days.A reporter for International Business
A report from Pew Research Center in 2015 found that in a sample of 929 cell phone users ages 13 to 17, the respondents sent and received an average of 67 texts per day while the median number of
Suppose you are testing to see whether human body temperatures tend to be lower than 98.6°F (what is thought to be the average body temperature) with the following hypotheses: H0: μ = 98.6°F, Ha:
According to the National Health Service (NHS), which provides healthcare for all UK citizens based on their need for healthcare rather than their ability to pay for it, the normal weight of a
Based on your answer to Exercise 2.4.12, what sort of conclusion can you make and how are you determining this? A. We have strong evidence that the difference in ages for husbands and wives is
Suppose you are testing to see whether bags of potato chips have an average weight that is larger than their label weight of 10 oz with the following hypotheses: H0: μ = 10 oz, Ha: μ > 10 oz.
A t-distribution looks a lot like a normal distribution, but it is a bit more spread out than a normal distribution with more observations in the “tails,” fewer in the middle. To determine
When assigning symbols to statistics and parameters, which of A–H is correct? (Choose all that are correct.) A. p is the sample proportion, π is the population proportion. B. x is the
Shift the sample data appropriately and find a p-value. A. 0.0001 B. 0.0491 C. 0.2518 D. 0.5014
Go to the Sampling Words applet and load some penny data by clicking the Pennies radio button located just to the right of the data window. This dataset contains the last two digits of the year on
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 A–C is least likely to happen? A. Randomly
Use the One Mean applet to take at least 10,000 samples from the MarriageAgesDiff data to develop a bootstrap sampling distribution for the mean. Which of A–D is the closest to the standard
Do you feel comfortable generalizing your conclusions to all cell phone users? If not, is there a population you feel you can generalize your conclusions to? Now suppose you asked 1,858 people
Use the One Mean applet, choose the Bootstrapping option at the top, and paste in the MarriageAgesDiff data. What are the mean and standard deviation for the data (with the appropriate
Which of A–D is FALSE? A. We use the symbol μ to represent the population mean. B. We use the symbol x to represent the sample mean. C. The symbols p and x are both used to
What are the appropriate null and alternative hypotheses for this study? A. H0: x = 0 years; Ha: x > 0 years B. H0: μ = 0 years; Ha: μ > 0 years C. H0: π = 0 years; Ha: π
Suppose instead of just asking the respondents whether they have ever faked a phone call, the interviewer said, “Research has shown that only 5% of adult Americans with cell phones have faked a
The administration at a local high school is considering building a new gym. In order to find out how the student body feels about this, a student organization decides to conduct a survey of the
When developing a bootstrap sampling distribution for a mean, we shift the sample data so it is centered on: A. 0. B. 0.50. C. The mean of the sample. D. The value of the mean in
Suppose instead of just asking the respondents whether they have ever faked a phone call, the interviewer said, “Many college students use apps that help them creatively fake a phone call. Have you

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