Questions and Answers of Introduction To Statistical Investigations

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
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 =

Showing 800 - 900 of 1041