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introduction to statistical investigations

Questions and Answers of Introduction To Statistical Investigations

Research on reducing stuttering in preschool children between the ages of 3 to 6 looked at 199 children who were registered in one of 20 participating speech therapy clinics throughout the
Refer to Exercise 5.2.43. Redo parts (d), (e), and (f) using the relative risk as the test statistic. Data from Exercises 5.2.43Are there differences in the efficacy of duct tape versus
Reconsider Exercise 5.1.16, along with this additional information: 17 senators are women Democrats. a. Produce a 2 × 2 table that classifies senators in the 2020 U.S. Senate according to party
The U.S. government authorizes private contractors to audit bills paid by Medicare and Medicaid. The contractor audits a random sample of paid claims and judges each claim to be either fully
Consider the four 2 × 2 tables, numbered 1–4. For each one the response is Yes/No and the explanatory variable is A/B a. Which two tables have the same pair of conditional
Data were gathered on 106 statistics students from a Midwestern college on variables including the sex of the respondent and whether they had eaten breakfast that morning. Which segmented bar graph
Suppose you are getting ready to run a two-proportion z-test to see whether students who have studied statistics are more likely to always wear seat belts in a car than those who haven’t studied
Using data from Exercises 5.2.3 and 5.2.4, use the Multiple Proportions applet to carry out a test of significance. Which of A–D is an approximate 2SD confidence interval? A. 0.082 to
Describe the parameters of interest in words. (You can use the symbol π to represent these parameters.)In 1970 Linus Pauling, a well-known chemist and Nobel Prize winning scientist, published
Using data from Exercise 5.2.3, which of A–D is the correct value for the appropriate statistic? A. 0.15 B. 0.25 C. 0.325 D. 0.40Data from Exercise 5.2.3Suppose you sample from
Which of A–D answers correctly calculates the relative risk for success in Group A compared to Group B (p?A/p?B) for the two-way table below?A. (10/60)/(20/60) = 1/2 B. (10/20)/(20/40) =
What are the variables that are measured/recorded on each unit?In 1970 Linus Pauling, a well-known chemist and Nobel Prize winning scientist, published Vitamin C and the Common Cold (1970), creating
Suppose you sample from two large populations and find sample proportions of p?1 = 120/300 and p?2 = 125/500. Suppose you are going to complete a test of significance using these proportions to see
What are the observational/experimental units?In 1970 Linus Pauling, a well-known chemist and Nobel Prize winning scientist, published Vitamin C and the Common Cold (1970), creating a great deal of
Suppose a 95% confidence interval for the difference in the proportion of female students who regularly drink coffee and the proportion of male students who regularly drink coffee (πF – πM) is
Which of A–D answers correctly calculates the difference in the proportions of success for Group A compared to Group B (p?A – p?B) for the two-way table below? A. (10/60) – (20/60) B.
Is this study an experiment or an observational study? How are you deciding?In 1970 Linus Pauling, a well-known chemist and Nobel Prize winning scientist, published Vitamin C and the Common Cold
Which type of distribution is used in a two-sample z-test? A. t-distribution B. Normal distribution C. Simulated null distribution D. Double proportion distribution E. None
Suppose you are testing to see whether the proportion of males who voted in the last election differs from the proportion of females who voted in the last election. Which of these is NOT a correct
Journal articles that describe some randomized experiment often include a table of the characteristics of the subjects after they were randomly assigned to the treatments, but before the treatments
State the research question. In 1970 Linus Pauling, a well-known chemist and Nobel Prize winning scientist, published Vitamin C and the Common Cold (1970), creating a great deal of public and
The validity conditions for a two-sample z-test include: A. You should have at least 10 successes and 10 failures in each group. B. Each group should have a sample size of at least
Student researchers at Hope 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 around campus, 232
In Exploration 4.2 you used the Randomizing Subjects applet to randomly assign subjects to two groups. At the end of the exploration, you blocked on a person’s sex and saw this eliminate the
Crohn’s disease involves chronic inflammation anywhere in the gastrointestinal (GI) tract. The disease is subdivided by where it occurs in the GI tract. Suppose a company is testing a new
Do your bananas get over-ripe too fast? It has been said that if you wrap the stem of a banana in plastic, it will last longer. A student experiment seeks to explore whether this is true. They bought
Are there side effects of watching 3D movies? More specifically, is nausea a side effect? A study done in Italy (Solimini, 2013) had moviegoers rate their levels of nausea on a 7-point scale after
Butterfat is the fat that naturally occurs in cow’s milk. For a product to be labeled whole milk, for example, it must contain at least 3.25% butterfat. Does the amount of butterfat vary with
The Physicians’ Health Study II was a randomized, double-blind, placebo-controlled study designed to “test alternate-day beta-carotene, alternate-day vitamin E, daily vitamin C, and a daily
The Physicians’ Health Study I was a very large, randomized, double-blind, placebo-controlled study designed to “test the effects of low-dose aspirin and beta-carotene on cancer and
Hurricanes in the United States are given names. Since 1979 both male and female names have been used, alternating between names that are typically thought of as male and those typically thought of
Students completing a project for their statistics class were testing whether, when blindfolded, subjects would be more likely to identify the flavor of an orange Starburst or a lemon Starburst. The
A drug manufacturer is testing a new headache drug. They recruit 100 subjects with headaches and have them rate the severity of their headaches on a scale of 1 to 10. The researchers randomly assign
A drug manufacturer is testing a new headache drug. They recruit 100 subjects with headaches and have them rate the severity of their headaches on a scale of 1 to 10. Based on the severity of the
A drug manufacturer is testing a new headache drug. They recruit 100 subjects with headaches and have them rate the severity of their headaches on a scale of 1 to 10. They give them the new drug and
Student researchers want to see whether students retain information better when they are taking notes by hand (with pen and paper) than on the computer, as some research suggests. Suppose they have
Causation. Is a cause-effect conclusion possible in this new study? Why or why not?The hypotheses are modified slightly for this new study: Null: The long-run proportion of men who will call the
To investigate whether there is an association between happiness and income level, we will use data from the 2018 General Social Survey (GSS), cross-classifying a person’s perceived happiness with
Fill in the two-way table with the data from the study.how to state null and alternative hypotheses for studies like this. Here they are for this study: Null: The long-run proportion of men who
A Pew Research Center poll conducted in 2017 found that 49% of respondents who were 65 years or older often get their news from network TV compared to 8% of 18- to 29-year-olds. a. Identify the
Which of the following are experiments? 1. Researchers ask subjects whether they drink coffee regularly and how much sleep they get per night to see whether there is an association between
You have a coin that you think is fair, with π = probability of heads = 1/2. To check, you plan to flip the coin n times. a. Compute the SD of p? for each value of n in the table and fill in
What is the main difference between an observational study and an experiment? A. Experiments must take place in a laboratory or a place where the responses of the experimental units can be
An experiment done in such a way that neither the subjects nor the researchers know which subjects are in the treatment group and which are in the control group is called: A. Double
Using the formula compute a 95% confidence interval for a population proportion given the sample proportion is 0.65 and the sample size is 500. Î± 1.96√p(1 − p)/n,
Using the formula compute a 95% confidence interval for a population proportion given the sample proportion is 0.35 and the sample size is 1000. P± 1.96√p(1p)/n,
The positive psychological benefit that many people experience simply from knowing they are receiving a treatment is known as the _____ effect. A. Placebo B. Doppler C.
Recall Question 4.1.1 about intrinsic motivation and position in the classroom. What types of variables are being analyzed? A. Both the explanatory and response variables are
Recall Exercises 3.1.29 and 3.1.30 about climbers on Mont Blanc. While diuretics were the most commonly found drug, hypnotic drugs were second. Hypnotic drugs are used to overcome insomnia. Sleeping
Exercise 3.1.29 described a method of collecting urine samples that the researchers thought would be representative of climbers on Mont Blanc. Because the observations were taken from urinals, we can
Exercise 3.1.26 gave the results of a national poll where 65% of a sample of 400 American independent voters responded that they support same-sex marriages. Use the One Proportion applet, repeatedly
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
Mont Blanc is the highest mountain in western Europe at 4,810 m, or 15,781 feet. The climb to reach the summit is not that technical so thousands attempt it each year. However, many of these climbers
Reconsider Exercises 3.3.24, 3.3.25, and 3.3.26 about the average number of states all students at the author’s school have visited. Using the data from the author’s sample, a 99% confidence
Student researchers wanted to determine the average reaction time for student athletes at their school. They used a reaction time applet that had students click a button on a computer as fast as they
The Exercise 3.1.24 gave the results of the poll where 64% of a sample of 2,737 adult Americans reported drinking at least one cup of coffee per day. Use the One Proportion applet, repeatedly testing
In a survey, 122 statistics students were asked how many siblings they have, and the results are the shown in the dotplot. The mean number is 2.172 siblings and the standard deviation is 1.328
IPSOS opinion and public research company surveyed 2,010 adult Americans and found that, on average, Americans have visited 12 states in the United States. In a survey of 136 statistics students at
Repeat parts (c) and (d) from Exercise 3.3.17 except construct a 99% confidence interval. How do the midpoints and widths of the 99% and 95% confidence intervals compare?Data from Exercises
A random sample of 16 college students was asked to report their mother’s height in inches and the results are shown in the dotplot. Would it be valid to use a theory-based confidence interval for
Repeat parts (c) and (d) from Exercise 3.2.14 but construct a 99% confidence interval. How do the width and midpoint of this confidence compare to the 95% confidence interval.Data from Exercise
Repeat part (c) from Exercise 3.2.12 but construct a 90% confidence interval. How do the width and midpoint of this confidence compare to the 95% confidence interval?Data from Exercises 3.2.12The
A random sample of 16 college students was asked to give the cost of their last haircut. The results in dollars are show in the dotplot. Would it be valid to use a theory-based confidence interval
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.
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
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, a
The Ipsos polling organization conducted a national survey in 2019, finding that 295 of the sample of 1,005 American adults had a tattoo. a. Use the Theory-Based Inference applet to determine a
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
Suppose you are calculating a 95% confidence interval for the average weight of a certain type of bag of potato chips. You collect a sample of 15 bags and find a mean weight of 10.15 oz. and a SD of
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
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
Suppose I am conducting a test of significance with H0: π = 0.50 and Ha: π ≠ 0.50 and I end up with a p-value of 0.02. I also construct 95% and 99% confidence intervals from my data. What will be
Suppose you have a dataset with the following summary statistics: n = 30, x? = 5.23, and s = 1.96. Also suppose a 95% confidence interval is constructed from the summary statistics. If you realize
Let π be some population proportion of interest and suppose a 99% confidence interval for π is calculated to be (0.18, 0.36) and a 95% confidence interval is calculated to be (0.20, 0.34). Suppose
According to a 2018 report by the U.S. Department of Labor, civilian Americans spend 2.84 hours per day watching television. A faculty researcher, Dr. Sameer, at California Polytechnic State
Suppose you are calculating a 95% confidence interval for the proportion of all students at your school who have ever taken piano lessons. You survey 100 students and find that 60% of them had taken
If you are testing the hypotheses H0: μ = 4 and Ha: μ ≠ 4, have a sample mean of 5 and get a p-value of 0.021, what can you say about a 95% confidence interval constructed using the same
Suppose you have a dataset with the following summary statistics: n = 500 and p? = 0.43. Also suppose a 95% confidence interval is constructed from the summary statistics. If you realize that the
If you are testing the hypotheses H0: μ = 3 and Ha: μ ≠ 3, have a sample mean of 2 and get a p-value of 0.341, what can you say about a 95% confidence interval constructed using the same
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
A Gallup survey of 1,100 randomly selected U.S. adults conducted June 2019 found that 53% of those surveyed were satisfied with the quality of education students receive in K through 12 grade in the
In Example 2.1, you saw that the percentage of people who said they voted in the 2016 presidential election from the General Social Survey (GSS) (69.8%) was significantly different than the
Students were asked how many cups of coffee they typically drink in a week. The results for 15 students is in the file Coffee. Put the data into the One Mean applet using the Bootstrapping option and
Recall from Exercise 2.4.31 about whether or not people recognize their face as being more attractive than it actually is. Because people often see their face in a mirror, the researchers wanted to
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
Recall from Exercise 2.4.29 on the predicted test scores. Redo parts (a) through (d) using median as the statistic instead of mean.Data from Exercises 2.4.29Right after 27 students in a college
Recall from Exercise 2.4.27 that the increase in joke ratings in the presence of a laugh track. Redo parts (a) through (d) using median as the statistic instead of mean.Data from Exercise
Right after 27 students in a college mathematics class were finished taking a test, they were asked to write down the score they thought they got on the test. After it was graded, their predicted
In the One Mean applet there are three populations of sleep times. All have a mean of about 8 hours and a SD of about 1.5 hours. a. Open up the applet and select Sleep 1. This represents a
Television shows often add laugh tracks to make the show seem funnier. Does doing the same thing with “dad jokes” make them funnier? The researchers (Cai et al., 2019) had a professional
Intelligence Quotient (IQ) is a score obtained from a standardized test that is supposed to measure human intelligence. The scores on these tests are designed so the median is 100 points and a
Put the data described in Exercise 2.4.25, FemaleTemp, into the Theory-Based Inference applet to answer (a)–(b). a. Again, we want to test to see whether average female body temperature is
For a given population of a single quantitative variable, by what factor must the sample size increase in order for the standard deviation of the sampling distribution of the mean to be half as large?
From the formula for the standard deviation of the distribution of sample means, SD of x? = σ ⁄√n, you can see that the standard deviation of the sample mean is affected only by the population
At some time in your life you may have gone to a doctor and had some sort of medical diagnostic test done like for strep throat or tuberculosis. These diagnostic tests can be related to hypothesis
Put the data described in Exercise 2.4.23, MaleTemp, into the Theory-Based Inference applet to answer (a)–(b). a. Again, we want to test to see whether average male body temperature is
What do you expect the means and standard deviations of the distribution of sample means to be when the samples are drawn from a large population with these parameters and sample sizes? a. μ =
The output shown for Exercise 2.2.21 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.
Recall Exercise 2.4.22 about male body temperatures. You should have found that 98.6°F was not a plausible value for the population mean because it was more than 2 standard deviations of the
A hypothesis test can be thought of like a criminal trial. When a person is charged with a crime, this person, the defendant, is either innocent or guilty. We can think of the null hypothesis as the

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