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introduction to statistical investigations

Questions and Answers of Introduction To Statistical Investigations

Consider the question of whether sick days in a company are equally likely to occur Monday through Friday. a. State the null and alternative hypotheses using symbols. b. If we conduct a
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.,
In a January 2019 poll conducted by the Pew Research Center, they asked a random sample of U.S. adults if they owned a cell phone. The results are shown in the following table by race. a. What
In a January 2019 poll conducted by the Pew Research Center, they asked a random sample of U.S. adults if they owned a smartphone. The results are shown in the following table by race.a. What
Reconsider Exercise 8.1.23 on cell phone use. Complete a test of significance to determine if there is an association between race and whether someone owns a cell phone using p?max − p?min as the
A study done in Germany (Willich et al., 1993) looked at which days of the week people had heart attacks. One subgroup the researchers looked at were those who were employed. They found that the 884
Researchers in Brazil explored the relationship between overconfidence and accuracy among Brazilian accountants (Cardoso, 2016). Based on a presurvey, the researchers classified their subjects as
Recall the study in Exercise 8.3.21 on which days of the week people experienced heart attacks. Another subgroup the researchers looked at were those who were not employed. They found that the 1,191
Does the color of a sign that asks someone to do something make a difference in a person’s obedience to that sign? This is what a student researcher investigated. There are double doors at the
In one set of Mendel’s pea experiments, he crossed a round-green pea with a wrinkled-yellow pea (Mendel, 1866). The result of this cross gave him a round-yellow pea. He then crossed two of these
In Exercise 8.1.21 about cell phone use, what if the question was “Are students more likely to be on their cell phones in the evening as they walk across campus than during the daytime?” How
Mendel took the 315 seeds from the round-yellow peas he obtained from the experiment given in Exercise 8.3.16 and planted them. Fourteen of the plants did not grow or did not produce seeds. Of the
Are college students more likely to be on their cell phone at certain times of day than other times as they walk across their campus? Student researchers explored this question. Of the 221 students
Recall Exercise 8.3.19 about dialysis patients dying of heart attacks. The researchers also looked at patients that had their dialysis done on Tuesday, Thursday, and Saturday and experienced cardiac
In 1938 Dr. Frank Benford, a physicist at General Electric, noticed that, given a list of numbers, more numbers started with the digit 1 than any other digit. He analyzed 20,222 sets of numbers
In another set of Mendel’s pea experiments, he crossed a purple-flowered pea plant with a white-flowered pea plant. This resulted in plants that were all purple-flowered. He then took these
One of the authors’ cell phones recently became able to state a random number when asked. The author wondered whether the phone’s method of picking a random number was truly random. He asked his
Student researchers asked 84 students whether they were willing to take a survey. Some of the students were offered an incentive of a candy bar and some were not. The summary of the results are
In addition to having dice pushed off a 2-inch ledge, as in the example in this section, the researchers also pushed dice off a 4-inch-high ledge with the following results.Is this an unfair way to
Recall Exercise 8.3.13 on commercial models and their eye colors. The researchers also explored the eye colors of registered commercial models in Brazil. They sampled from 400 profiles of females
Do female models have eye colors that are distributed differently than those of the population of their country? That is a question that UK researchers were interested in exploring (Forti, 2016).
A random sample of 100 high school students was taken and the following table gives a summary of their responses when they were asked what their favorite season is. We are interested in testing to
Calculate the chi-square test statistic for the following datasets and null hypotheses. a. H0: πA = πB = πC = 1.3 b. H0: πA = πB = πC = 1.3 Observed count Category A B C 12 16
Consider doing a chi-square goodness-of-fit test with the null hypothesis of π1 = π2 = π3 = 1/3 on two different sets of data. For categories 1, 2, and 3, respectively, dataset A has observed
What data type is used in a chi-square goodness-of-fit test? How does that compare with the type of data used in the type of chi-square test you did in Section 8.2?
Calculate the chi-square test statistic for the following datasets and null hypotheses a. H0: The population is distributed in a ratio of 1:2:1 for the categories A, B, and C, respectively.b.
The following distributions represent colors of 100 candies. You want to run a chi-square goodness-of-fit test with the null hypothesis that the distribution of colors is evenly distributed. Which of
In running a chi-square test of significance on the data from the graph in Exercise 8.2.3 about comparing coffee drinking between where students live, which of A-E is the appropriate way to write the
State the null and alternative hypotheses to be investigated with this study. (You may use the symbol π to represent these parameters.) The following table provides descriptive statistics on the 152
Suppose you complete a chi-square test to see whether there is a difference in the proportion of Republicans, Democrats, and Independents that favor a new law and get a p-value of 0.01. You then
The summarized data from a survey of college students, in which they were asked where they live (Dorm, College apartment, or Off campus) and whether or not they regularly drink coffee are shown in
Using the data in the following table, what is the chi-square test statistic? A. 0.93 B. 4.93 C. 5.38 D. 8.13 E. 484.93 Category A B C D 39 20 Observed count 10 51 Expected
Suppose we are comparing three proportions using a chi-square test. If the data are adjusted so the proportions are farther apart (but the sample sizes stayed the same for each condition),
Recall Exercise 8.2.2 on where students live and whether they regularly drink coffee. The results of the survey are shown in the mosaic plot. Which of these would you predict to be the findings if a
College students were asked to rate their abilities as drivers and how often they text while driving, with the summarized data shown in the Exercise 8.2.1 table. Are validity conditions met for a
Suppose you are running a chi-square goodness-of-fit test on a dataset that has five categories and you calculate a chi-square test statistic of 7.46. What is the corresponding p-value? A.
Partial results of a survey of college students, in which they were asked where they live (dorm, college apartment, or off campus) and whether they regularly drink coffee are shown in the following
Which of A–E is the proper way to write out the alternative hypothesis for the test from Exercise 8.3.1 on candy flavor distribution? A. The long-run percentages of candies are distributed 50%
The flavors of a certain kind of candy are supposed to be distributed as follows: 50% cherry, 30% lemon, and 20% orange. You randomly sample 180 of these candies to run a chi-square goodness-of-fit
Completing a chi-square test on a 2 × 2 table is equivalent to what other type of test (with a two-sided alternative)? A. One-proportion z-test B. Two-proportion z-test C. One-sample
Seagulls are notorious for stealing food from people. Will staring at them be a deterrent? Researchers (Goumas et al., 2019) set French fries in a sealed plastic bag on the ground and then crouched
Researchers in Australia (Rogers et al., 2019) investigated whether tattoos affect sweat rates when exercising. They recruited 22 subjects, each with a tattoo that was more than 2 months old, larger
Recall Exercise 7.2.40 on the effect of music on chimpanzees. The researchers also kept track of the total number of aggressive events each chimpanzee displayed and divided these by the total time
Reconsider Exercises 7.2.37 and 7.2.38 on time headway variability. If you haven’t done so, put the data file TimeHeadwayVariability in the Matched Pairs applet and do at least 1,000
Reconsider Exercise 7.2.37 on time headway variability. If you haven’t done so, copy and paste the data from the file TimeHeadwayVariability into the Matched Pairs applet and do at least 1,000
Recall Exercises 7.2.33, 7.2.34, and 7.2.35 in which researchers explored the effects on driving with various types of cell phone use. In particular, they were interested in comparing the effects of
Recall Example 7.3 about adding a laugh track to dad jokes to make them funnier. The researchers investigated two kinds of laugh tracks—one with posed laughter and one with spontaneous laughter.
Reconsider Exercises 7.2.33 and 7.2.34 on braking reaction time. If you haven’t done so, put the data file BrakeReactionTime in the Matched Pairs applet and do at least 1,000
Reconsider Exercise 7.2.33 on braking reaction time. If you haven’t done so, put the data file BrakeReactionTime in the Matched Pairs applet and do at least 1,000 randomizations. a. What is
A study done by Jung et al. (2014) looked at hurricane names and the perceived threat. The researchers thought that hurricanes in the United States with male names would differ in perceived danger
Researchers at Arizona State University (McNabb & Gray, 2016) explored the effects on driving with various types of cell phone use. In particular, they were interested in comparing the effects
Student researchers wanted to see whether listening to music with lyrics would affect a person’s ability to memorize words compared to listening to music without lyrics. They recruited 31 people
Student researchers wanted to explore whether a person’s ability to memorize objects is affected by whether they are shown the objects in pictures that are in color or pictures in black and white.
Reconsider Exercise 7.2.18 about rating bottled and tap water. a. Use the 2SD method to determine an approximate 95% confidence interval for the mean difference in water ratings (bottled –
Recall Exercise 7.3.30 about music and the Stroop test. a. Put the data into the Matched Pairs applet to find the sample mean, sample standard deviation, and sample size of the
Is a basketball player’s ability to make free throws different when they get their own rebound or when someone else gets their rebound for them? This is what student researchers wanted to explore.
Do people think bottled water tastes better than tap water? In a blind taste test, student researchers asked 31 subjects to rate the taste of two waters, one bottled and one tap, on a scale from 1 to
When you hand in your test, do you think you will get a higher score than you actually do? A professor collected data to answer this question in a college mathematics course. After finishing a test,
Student researchers wanted to see whether listening to music would affect the time it takes people to complete a Stroop test. In a Stroop test, words of colors are shown printed in a color that does
Suppose your research question is: Can people better memorize 10 objects if they are shown the objects in pictures or in words? Describe how you could set up and run an experiment to answer this
Reconsider Exercise 7.2.16 about rebounding free throws. a. Use the 2SD method to create an approximate 95% confidence interval for the mean difference in number of shots made (rebounded –
Which of these is the correct way to calculate the standardized test statistic for a one-sample t-test for paired data with x?d = 2.3, sd = 1.8, and n = 35?A.B.c.D.E. t= 2.3 1.8/√/35
In Exercise 7.2.13 the statistic used was the mean of the difference in ages (husband’s age − wife’s age). Explain how the following things would change (or not) if you used the mean of the
Which of these is an appropriate way to write out the null hypothesis in symbols for a test for paired data with a quantitative response? A. H0: x?d = 0 B. H0: p?d = 0 C. H0: πd =
With paired data: A. The mean of differences is always the same as the difference of the two group means, and the standard deviation of the differences is always the same as the difference of
The following set of dotplots with overlaid boxplots gives the cost of the most recent haircut for 20 male college students (top) and 20 female college students (bottom) in a statistics class. The
For which of these would you, most likely, want to use a paired design for the study? A. Compare males and females on how many Facebook friends they have B. Compare the income levels of
Suppose you are calculating a 95% confidence interval for the mean difference using paired data to compare the number of words memorized by people while listening to music compared to the number of
Suppose you plan to conduct an experiment to compare reaction times when getting a visual cue versus an auditory cue. Your friend wants to test 40 people, 20 under each condition (randomly deciding
Which of these is the correct way to calculate an approximate 95% confidence interval for the mean difference based on paired data with x?d = 3.5, sd = 2.4, and n = 40? A. 2.4 ± 2(3.5/
Suppose you are testing the hypotheses H0: μd = 0 and Ha: μd ≠ 0 in a paired-design and obtain a p-value of 0.21. Which one of A–D could be a possible 95% confidence interval for μd?A. −2.30
Student researchers at Hope College conducted an experiment to determine whether there is a difference in memorization ability of students when they take notes on paper using handwriting versus
Recall Exercise 6.2.37 on inhibitory control. Besides keeping track of the total time it took the animals to reach the food, the researchers also kept track of the amount of time the animals spent at
The following set of dotplots with overlaid boxplots gives the number of pairs of flip-flops students said they owned for 13 males (top) and 37 females (bottom) in a statistics class. The five-number
Student researchers tested to see whether listening to music while memorizing words would interfere with a person’s ability to memorize words. Their subjects were randomly assigned to either listen
Researchers Marshall-Pescini et al. (2015) compared identically raised pack dogs and wolves on inhibitory control. To do this, a v-shaped fence constructed of wire mesh was set up with a food item (a
Researchers Chaddock-Heyman et al. (2015) investigated the role of aerobic fitness in mathematical achievement in preadolescent children. They had 24 children in their high fitness group (>70th
Recall Exercises 6.2.34 and 6.2.35 about comparing distances traveled by captive African and Asian elephants. a. Put the data in the Multiple Means applet to create a null distribution and from
A study done by Jung et al. (2014) looked at hurricane names and their perceived threat. They thought that if hurricanes in the United States had male names they would be perceived as more dangerous.
Statistics students wanted to see whether there was an association between whether students eat breakfast daily and their grade point average (GPA). They surveyed 106 students at their college and
Recall Exercise 6.2.34 about comparing distances traveled by captive African and Asian elephants. a. Put the data in the Multiple Means applet to create a null distribution and from it calculate
Listed below are the number of cups of coffee 25 students in a college statistics class said they drink per week. 1, 14, 4, 13, 10, 14, 10, 5, 18, 21, 26, 20, 10, 6, 1 ,7, 10, 1, 12, 2, 3, 16,
Similar to Exercise 6.3.33, researchers Dumas and Dunbar wanted to compare creativity of students with different majors at their university, specifically biology and theater. As a measure of their
Researchers Holdgate et al. (2016) studied walking behavior of elephants in North American zoos to see whether there is a difference in average distance traveled by African and Asian elephants. They
Researchers Dumas and Dunbar wanted to see whether stereotypes related to creativity can influence the creativity of a subject (2016). The 64 subjects were randomly placed into two groups of 32 each.
Recall Exercises 6.2.31 and 6.2.32 about memorizing words by a group that was listening to music compared to a group that was not listening to music. a. Put the data in the Multiple Means applet
a. Construct a 95% confidence interval for the difference in the mean evacuation ratings between the female-named hurricane (Christina) and the male-named hurricane (Christopher) and describe what it
Recall Exercise 6.2.31 about memorizing words by a group that was listening to music compared to a group that was not listening to music.a. Put the data in the Multiple Means applet to create a null
A study by Junget al. (2014) looked at hurricane names and their perceived threat. They thought that if hurricanes in the U.S. had male names they would be perceived as more dangerous. In one part of
Student researchers tested to see whether listening to music would interfere with a person’s ability to memorize words. Their subjects were randomly assigned to either listen to music or not. They
Reconsider Exercises 6.3.26–6.3.29. a. If the sample responses had shown more variability in each group (say, SD of 2 in each group) and all else had remained the same as originally, what
Recall Exercises 6.2.28 and 6.2.29 about comparing quiz scores between students taking notes on paper versus the computer. a. Put the data in the Multiple Means applet to create a null
Reconsider Exercise 5.CE.16. Using the same data but grouping “routine” with “exciting” rather than with “dull” produces the following 2 × 2 table: Analyze these data to investigate
Recall Exercise 6.2.28 about comparing quiz scores between students taking notes on paper versus the computer. a. Put the data in the Multiple Means applet to create a null distribution and from
Student researchers at Hope College conducted an experiment to determine whether students memorize material better if they are taking notes on paper using handwriting as opposed to taking notes on a
An article that appeared in the British Medical Journal (2010) presented the results of a study conducted by researcher Jeremy Groves, whose objective was to determine whether the type of frame of
For Exercise 6.1.19 on students sending texts, are there any outliers in the distribution according to the 1.5 × IQR rule? If so, which ones? Data from Exercise 6.1.19Twenty college students
Twenty college students were asked how many texts they send on a typical day and the results are shown below. 3, 4, 5, 10, 10, 10, 20, 20, 30, 30, 30, 50, 50, 55, 75, 75, 100, 150, 200,
The 2020 U.S. Senate consists of 75 men and 25 women. The 2020 U.S. Senate consists of 53 Republicans and 47 Democrats (counting 2 Independents as Democrats because they vote with Democrats more than
What are the five parts of the five-number summary?

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