Chapter 11 Exercises

Clarifying the Concepts

Question 11.1

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Question 11.2

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Question 11.3

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Question 11.4

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Question 11.5

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Question 11.6

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Question 11.7

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Question 11.8

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Question 11.9

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Question 11.10

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Question 11.11

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Question 11.12

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Question 11.13

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Question 11.14

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Question 11.15

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Question 11.16

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Question 11.17

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Question 11.18

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282

Question 11.19

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Calculating the Statistic

Question 11.20

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Mean test grades Students in the front Students in the back
Class 1 82     78    
Class 2 79.5 77.41
Class 3 71.5 76    
Class 4 72     71.3

Question 11.21

Consider the following data from two independent groups:

Group 1: 97, 83, 105, 102, 92

Group 2: 111, 103, 96, 106

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  2. Dpk+3Y/V0KEcDUF61dRgskz5lxdrPNOqXtCc0ubTlV28sHSM7WO7ssh5Wvuckjk3xMzxkLb4+br70xpMUWObYtkjgeVYklh9pb/7G8sSRkn0eHFphJ4569CuEhhcBJXfOoILqAcYflTpMF9y
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  4. sOTFS+uUl9ouYl68q41rVUO9/nq1nvOQhSBdoCUJcQ/ze7LwsXq1TMlTKhpioyzBO9Jql9tOikhWl/cQmX1gN/PZ14nLwWQcWQDd0ua3zX43SaY4uTT4/OdJ/bDC1D7L1LNi8m8fmJ4J45VlObgjcRNsZq7Ul8bi2cBTUen8wG4IvB7fa6pLUQ04qOiPyPd2yQnNC3sa88Sya9AQ4j36EcBDgxiDfozZiU8sugVdK/lFW4mz
  5. 72/37JzeGkWre4bPoVYdNKo4bfW7eCDRNm7HY6cacs/1eTHSdscYZcEjHEmYc9z3XERQ/XkUnJo5nkzGA5Si18p5F8NW8vw04FMTwQjopv0=
  6. ji/Qi5rMiaF6bbOpkY7GPKs8ENNUOfIqXUeo2sEkROwW4PWDSU+wbpPlrJF00cQ6YiRetvmdI7ZumleG9XgvyejNPp0KQ9/Gp5O6R9UXhh5ytrgy9BdIsAgLamV0WhAIoNT4ldtuFYFnhg+T8Oka2azqMXY=
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Question 11.22

Consider the following data from two independent groups:

Liberals: 2, 1, 3, 2

Conservatives: 4, 3, 3, 5, 2, 4

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  5. 72/37JzeGkWre4bPoVYdNKo4bfW7eCDRNm7HY6cacs/1eTHSdscYZcEjHEmYc9z3XERQ/XkUnJo5nkzGA5Si18p5F8NW8vw04FMTwQjopv0=
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Question 11.23

Find the critical t values for the following data sets:

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  2. 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
  3. 48Xd6COqkzPZyyOnTkWF3zU+PlGVdzDLGGetzqq+t/M96w2+B1af9JGVh0VLwA+EuumcsP7bN35xqViTRkderIgW8cOeAbihr//kyLmU6RPTF8rv0HAaKTL0MNZa/NfHHyxzpC/Gk8PgYJg+VMrtbxFF3mo+tunT9/eRJpo261mY3cE7T++UuNgUdnGTtVi4kyHUploL1L62ws2C6ojalQ==

Question 11.24

Use the following data set to answer the questions below:

15 24 35 16 18 22 16 72

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  2. Ra9r8fKdzSvabCRfQAUhbS0NU9EKTJn5jZfzD3Mu0wuRmf3HDObfpZosBqR7DijNjQwe91sHbZktSyp2F5PlkaK+eWNe092m
  3. GiAtsN4nODfApALjgEsKuqoqXTyAT318PExBEgyVYjJZmsUj/AusSb7vWkUcHjAOoNGDRrN6ESTDnVzhMFrKLJlkZda7cZMsokq3pLSCSHRxA3VSjzT/7IWTekUZSvXgVbGdo6ooVgx/dQgWEhYRwigEoYopdhmCJGwo37w9MgMjqJzFhtN4omjnq2j4iPJjMK8FyO7MHQ0us4eixXH821yjvf9Z9f59Nt6glfeiilNWqWs9WxXSeRIDZOaI+7H/5BxxoLrWXik=

Question 11.25

For each of the following sets of data, indicate whether you would apply a square root transformation to the data and explain why you would or wouldn’t.

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  2. glCLQ7DsSrJcFCzQyhgqXz0VFzXbKL4QgJ2uiH+40Hwwrwyps/pPmN1eNfE=
  3. ZGcKBGw1tXkbxv0997c2Xi5iIQdNMIb3of0vOwZeI0r5Jo+fUKO62Ugei/1RHw6I

Applying the Concepts

Question 11.26

Making a decision: Numeric results for several independent-samples t tests are presented here. Decide whether each test is statistically significant, and report each result in the standard APA format.

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  2. kfhcZuTXbS8g4Bm5/DgCeMwKvkntfBhewYqvpzF0BdHqZjGlNkID9lK58qsoZPy/cE7F+WZV7l+/RuQ0W5jWIkQQVjBAUW/z0tWfnPO4n4j31XMwAKztXdVe7IhybO0oX3vjLocqRmRR4Awl3L+siIOS/jdwkKuaknp03ZDFRv6C3SUfeQp0eZ35EbyybbpnosaWeQFJmqkl8SEI3dcG1x+f+qm3D5t3M5/QnF93CBWKvSuXOOqTITa22iE+D9uQE9mofPNvVA/GCT8IrPl/NgiMl9KGWAAj6u9wU9gQy4wjZydp9DoKDjvzm6fMxFQD/tgvMT/4Nlvb3VBsGrBLGOTPgIDFhQI2t3TjnA==
  3. v4Nfb3zeAct/ubihYj+UUqhcoW+mWIh3aZoEZ72pN7eRqnW99oPFdcQJffpxjek0GIg95Ph91JY7NwvxXgg8nHAtuaFTQHe8XaH03vz+IGM8U7YLJcVI0Rp0b5MqPKP4DbcxTO3GCrQjPi1niDGcDQM+SfTBb4ZBk66cSIuko3VXkZTETr8bAFghY3HQq7ZO2QemtSGWSIn3hFhfveQl9ymYINdsGf6aWUf2cKsol33BWvpbxd6Rp7WkhGmLqGsK9XhymDyIqeI9quxOzt5Q370HPBvphr+dbOlquhUcAw1l0QE8

Question 11.27

The independent-samples t test, hypnosis, and the Stroop effect: Using data from Exercise 10.29 on the effects of posthypnotic suggestion on the Stroop effect (Raz, Fan, & Posner, 2005), let’s conduct an independent-samples t test. For this test, we will pretend that two sets of people participated in the study, a between-groups design, whereas previously we considered data from a within-groups design. The first score for each original participant will be in the first sample—those not receiving a posthypnotic suggestion. The second score for each original participant will be in the second sample—those receiving a posthypnotic suggestion.

283

Sample 1: 12.6, 13.8, 11.6, 12.2, 12.1, 13.0

Sample 2: 8.5, 9.6, 10.0, 9.2, 8.9, 10.8

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  10. LL3Gvjy4ew3DYgHwrmJOenFFMj2loL8uhf1nzAjE/vMb7T163ZcxyFuvSQKie0Gs2sfyuygCC2Qdwm2gIfq96eNKeBVKsS2UtwAHIWO+BMereCoz1FRHMHGNLDYyz59X
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Question 11.28

An independent-samples t test and getting ready for a date: In an example we sometimes use in our statistics classes, several semesters’ worth of male and female students were asked how long, in minutes, they spend getting ready for a date. The data reported below reflect the actual means and the approximate standard deviations for the actual data from 142 students.

Men: 28, 35, 52, 14

Women: 30, 82, 53, 61

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Question 11.29

An independent-samples t test, gender, and talkativeness: “Are Women Really More Talkative Than Men?” is the title of a 2007 article that appeared in the journal Science. In the article, Mehl, Vazire, Ramirez-Esparza, Slatcher, & Pennebaker (2007) report the results of a study of 396 men and women. Each participant wore a microphone that recorded every word he or she uttered. The researchers counted the number of words uttered by men and women and compared them. The data below are fictional but they re-create the pattern that Mehl and colleagues observed:

Men: 16,345 17,222 15,646 14,889 16,701

Women: 17,345 15,593 16,624 16,696 14,200

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Question 11.30

An independent-samples t test, “all-inclusive” resorts, and alcohol consumption: At some vacation destinations, “all-inclusive” resorts allow you to pay a flat rate and then eat and drink as much as you want. There has been concern about whether these deals might lead to excessive consumption of alcohol by young adults on spring break trips. You decide to spend your spring break collecting data on this issue. Of course, you need to take all of your friends on this funded research trip, because you need a lot of research assistants! You collect data on the number of drinks consumed in a day by people staying at all-inclusive resorts and by those staying at noninclusive resorts. Your data include the following:

284

All-inclusive resort guests: 10, 8, 13

Noninclusive resort guests: 3, 15, 7

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Question 11.31

An independent-samples t test and “mother hearing”: Some people claim that women can experience “mother hearing,” an increased sensitivity to and awareness of noises, in particular those of children. This special ability is often associated with being a mother, rather than simply being female. Using hypothetical data, let’s put this idea to the test. Imagine we recruit women to come to a sleep experiment where they think they are evaluating the comfort of different mattresses. While they are asleep, we introduce noises to test the minimum volume needed for the women to be awakened by the noise. Here are the data in decibels (dB):

Mothers: 33, 55, 39, 41, 67

Nonmothers: 56, 48, 71

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Question 11.32

Choosing a hypothesis test: For each of the following three scenarios, state which hypothesis test you would use from among the four introduced so far: the z test, the single-sample t test, the paired-samples t test, and the independent-samples t test. (Note: In the actual studies described, the researchers did not always use one of these tests, often because the actual experiment had additional variables.) Explain your answer.

  1. l++CYVDuY72u7iwhX4FHBFYxZDSkEbdtmY4WyuXUmKBM/s4zTNDsS9G5APRfWdsslmUBLLjhYJQ2ab8DpHBjiYqnZca6x5gj+ZzlpAHVNQdPW4F2P21AWPuhzayd0LyouS72bm6fHX9ksHHPd73v0LL9/iiVcarNsyZh8KYOOrkOLYHLiEMYWX0a7q3UiOmW2xV0YX06OKCixNuVRkIKCUywT1Mdie5LSSw6XrjFvzL6HF4qrdVv/MrAt1YAKx9b91pl/DY6zuaI2XyeBTxTw9+OariMJ5eRq5yTJ9HM0LeEhSkzZIcNvnMLGY2Av9ElO9BZWK/39kiF+UPgUt47uLxxUXgzHRYYDmoYyUIItT46i9yQJVkON9zsK22AxrBZKuacoejCdgWFMwPZg93s7WtpkITKfA79bBGp/Aa5U6/ba1fu3QSpB+1ueVRJcJvUQSvZyw7/lZ0oEnqVStXhJo5uH1dkUHseh5Cq5Q==
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Question 11.33

Choosing a hypothesis test: For each of the following three scenarios, state which hypothesis test you would use from among the four introduced so far: the z test, the single-sample t test, the paired-samples t test, and the independent-samples t test. (Note: In the actual studies described, the researchers did not always use one of these tests, often because the actual experiment had additional variables.) Explain your answer.

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Question 11.34

Null and research hypotheses: Using the research studies described here (from Exercise 11.33), create null hypotheses and research hypotheses appropriate for the chosen statistical test:

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Question 11.35

Independent-samples t test and walking speed: The New York City Department of City Planning (2006) studied pedestrian walking speeds. The report stated that pedestrians who were en route to work walked a median of 4.41 feet per second, whereas tourist pedestrians walked a median of 3.79 feet per second. They did not report results of any hypothesis tests.

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Question 11.36

Independent-sample t tests and “the fun theory”: Volkswagen has created a series of videos based on its “fun theory,” the idea that you can change behavior if you take an activity that is good for society and make it fun. (You can watch the videos at http://www.thefuntheory.com/.) For each of the following examples, state the independent variable (and its levels) as well as the dependent variable (and the types of variables that both of these are). Then, state whether you could use an independent-samples t test to analyze the data, and explain your answer.

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Question 11.37

Cafeteria trays, food consumption, and an independent-samples t test: Kiho Kim and Stevia Morawski (2012) reported the following in the abstract (brief summary) of their published research study: “Here, we report on the results of an experiment to evaluate the effects of tray availability on food waste production and dish use in a university dining facility. We sampled 360 individual diners over a 6-day period and documented a 32% reduction in food waste and a 27% reduction in dish use when trays were unavailable.”

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286

Putting It All Together

Question 11.38

Gender and number words: Chang, Sandhofer, and Brown (2011) wondered whether mothers used number words more with their preschool sons than with their preschool daughters. Each participating family included one mother and one child—either female or male. They speculated that early exposure to more number words might predispose children to like mathematics. They reported the following: “An independent-samples t test revealed statistically significant differences in the percentages of overall numeric speech used when interacting with boys compared with girls, t(30) = 2.40, p < .05, d = .88. That is, mothers used number terms with boys an average of 9.49% of utterances (SD = 6.78%) compared with 4.64% of utterances with girls (SD = 4.43%)” (pp. 444–445).

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Question 11.39

School lunches: Alice Waters, owner of the Berkeley, California, restaurant Chez Panisse, has long been an advocate for the use of simple, fresh, organic ingredients in home and restaurant cooking. She has also turned her considerable expertise to school cafeterias. Waters (2006) praised changes in school lunch menus that have expanded nutritious offerings, but she hypothesizes that students are likely to circumvent healthy lunches by avoiding vegetables and smuggling in banned junk food unless they receive accompanying nutrition education and hands-on involvement in their meals. She has spearheaded an Edible Schoolyard program in Berkeley, which involves public school students in the cultivation and preparation of fresh foods, and states that such interactive education is necessary to combat growing levels of childhood obesity. “Nothing less,” Waters writes, “will change their behavior.”

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Question 11.40

Perception and portion sizes: Researchers at the Cornell University Food and Brand Lab conducted an experiment at a fitness camp for adolescents (Wansink & van Ittersum, 2003). Campers were given either a 22-ounce glass that was tall and thin or a 22-ounce glass that was short and wide. Campers with the short glasses tended to pour more soda, milk, or juice than campers with the tall glasses.

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