Questions and Answers of Introduction To Statistical Investigations

Suppose a friend of yours says she is a 75% free-throw shooter in basketball. You don’t think she is that good and want to test her to gather evidence that she makes less than 75% of her free
Suppose you are testing the hypotheses H0: π = 0.50 versus Ha: π > 0.50. You get a sample proportion of 0.68 and find that your p-value is 0.02. Now suppose you redid your study with each of the
Suppose you are testing the hypotheses H0: π = 0.50 versus Ha: π > 0.50. You get a sample proportion of 0.68 and find that your standardized statistic is 2.53. Now suppose you redid your study
Suppose a friend of yours says she is a 75% free-throw shooter in basketball. You don’t think she is that good and want to test her to gather evidence that she makes less than 75% of her free
Student researchers were interested in whether people will be more likely to choose the name-brand cookie (Chips Ahoy) over the store-brand (Chipsters) in a blind taste test. They tested this with 20
You have heard that in sports like boxing there might be some competitive advantage to those wearing red uniforms. You want to test this with your new favorite sport of chess-boxing. You randomly
LeBron James of the Los Angeles Lakers hit 558 of his 1,095 field goal attempts in the 2018/2019 season for a shooting percentage of 51.0%. Over the lifetime of LeBron’s career, can we say he is
You should have seen that if the sample size is large enough, the distribution of sample proportions will have a standard deviation of From this formula you can see that the SD of is p̂
Suppose you are testing the hypotheses H0: π = 0.50 and Ha: π > 0.50 and get a sample proportion of 0.65. From this, you compute a standardized statistic and a p-value. If your sample proportion
If Kevin Durant of the Golden State Warriors hits 52 out of his first 100 field goals in the 2018/2019 season, let’s see how we might investigate if he is more likely than not to make a field
Reconsider Exercise 1.2.9 about your friend shooting free throws. Which of A–E is the appropriate sample statistic and proper symbol? A. p̂ = 0.75 B. π = 0.75 C. p̂ = 0.65 D.
Kevin Durant of the Golden State Warriors hit 721 of his 1,383 field goal attempts in the 2018/2019 season for a shooting percentage of 52.1%. Over the lifetime of Kevin’s career, can we say that
You have heard that in sports like boxing there might be some competitive advantage to those wearing red uniforms. You want to test this with your new favorite sport of chess-boxing. You randomly
Reconsider Exercises 1.2.9 and 1.2.10 about your friend shooting free throws. You run this test and find a p-value of 0.1150. Which of A–E is the best way to state the conclusion? A. Because
What is a z-statistic?
Suppose we obtain a p-value of 0.2020, we can say we have: A. Little to no evidence against the null hypothesis. B. Strong evidence for the null hypothesis. C. Moderate evidence
Suppose you are testing the hypotheses H0: π = 0.25 and Ha: π < 0.25 and the observed statistic, p̂ is equal to 0.30 with a sample size of 100.a. If you are using a proportion as your
Explain the meaning of each of the symbols in (a)–(e). a. H0 b. Ha c. p̂ d. π e. n
What is the difference between p̂ and the p-value?
Suppose that, unbeknownst to you, 60% of the students at your large school typically ride the bus to school. You and a friend are taking random samples of students to estimate this proportion. You
Although we know some animals, like dogs, have a keen sense of smell, what about humans? A woman from Scotland, Joy Milne, claimed that she was able to determine whether someone had Parkinson’s
Statistics students were asked to randomly pick a whole number between 1 and 10. Sixty-two out of 101 students picked a number greater than 5. If they truly randomly picked their numbers, we would
Many types of studies have been done to see whether animals have a sense of number. In one study (Beran & Beran, 2004), researchers wanted to see whether chimpanzees could remember how many items
Although we know some animals, like dogs, have a keen sense of smell, what about humans? A woman from Scotland, Joy Milne, claimed that she was able to determine whether or not someone had
Recall Exercise 1.2.30 about chimpanzees having a sense of number. Besides testing Mercury, the researchers also tested three other chimpanzees. One, named Lana, picked the container that held 4
Patients with kidney disease often have a procedure called dialysis done to clean their blood if their kidneys can’t do this properly. This procedure is often done three days per week, with Monday,
Blindsight is a condition in which people are blind but can still respond to things they cannot consciously see. A patient (who had suffered brain damage and whom researchers Persaud et al. called GY
Many types of studies have been done to see whether animals have a sense of number. In one study (Beran & Beran, 2004), researchers wanted to see whether chimpanzees could remember how many items
Recall Exercise 1.5.31 on cardiac arrests for kidney disease patients. Besides the Monday-Wednesday-Friday schedule for dialysis, many patients are on a Tuesday-Thursday-Saturday schedule. Again,
Researchers, reporting in Chemical Senses (Roberts et al., 2005), were interested in body odor as it relates to genetics. They compared body odor between adult identical twins that were not living
Recall Exercise 1.3.31 about GY and blindsight. To test GY’s awareness of whether he correctly identified whether the square was present or not, they had him wager on whether or not he thought he
Whereas flipping a coin should result in 50% heads and 50% tails in the long run, will spinning coins on a table give the same result or not? Test this with a coin of your choice, making sure you
Recall Exercise 1.2.22 about identical twins and similar body odors. The researchers in this study also ran the same kind of test using non-identical female twins. The 113 sniffers were given a pad
People use animals to predict outcomes of sporting events and elections mostly by having the animals pick between two containers of food, each representing one of the two teams or the two candidates
In 2007, NBA referee Tim Donaghy was suspected of collaborating with a bookie to fix games in which he was refereeing. To help fix a game, a referee could call more fouls on one team which would
In Exploration 1.1 you looked at data involving the dog Harley picking one of two cups that the experimenter bowed toward. Another dog in that study named Jango, a male black lab, went to the cup
In the first election of the 20th century, Theodore Roosevelt (178 cm) defeated Alton B. Parker (175 cm). There have been 28 additional elections since then, for a total of 29. Of these, 26 elections
Do dogs pick up information by eavesdropping on interactions between people? Researchers in Argentina (Freidin, et al., 2013) wanted to see whether dogs would show a preference for people based on
Recall Exercise 1.5.34 that introduced the binomial distribution as an exact theory-based distribution to model the types of situations you have seen in Chapter 1. Two of the other dogs in the
In this exercise, as in Exercise 1.4.34, we eliminate elections with more than two major party candidates as well as elections with two candidates of the same height. In addition, we eliminate the
Recall Exercise 1.3.34 on eavesdropping dogs. In another test, the researchers had the beggar and the donors perform the exact same tasks except the beggar did not say anything. When 15 dogs watched

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