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Statistical Analysis Questions - Hypothesis Tests and Confidence Intervals

## Question 1- Memory Recollection Study

1.A study is conducted to determine whether a new drug will improve memory. A person taking the new drug is able to recall 35 words from a list of 50 after studying the list for 10 minutes. Do they recall more words than the general population that can recall only μ = 25 words?

b. What was the null hypothesis in words and symbols?

c. What was the alternative hypothesis in words and symbols?

2.What is the z-critical value for each of the following?

a. α = .05, one-tailed test

b. α = .01, two-tailed test

c. α = .01, one-tailed test

3.  A diligent researcher found that the typical person spends a population mean amount of µ = 25 hours per week using the Internet, with a population standard deviation of σ = 2.5 hours. The researcher took a random sample of n = 25 Time Warner cable customers and found that they spend a sample mean amount of M = 26.5 hours per week on the Internet. Do Time Warner cable customers spend more time on the Internet than the general population?

Conduct the appropriate hypothesis test using α = .05 and state your conclusion in terms of this problem. Make sure to use APA style conclusions (as shown in PowerPoint lectures)

4.  An urban economist wishes to estimate the mean amount of time spend traveling to work. They obtain a random sample of n = 50 individuals who are in the labor force and find that the sample mean travel time is M = 24.2 minutes. Assuming the population standard deviation of travel time is σ = 18.5 minutes, construct and interpret a 95% confidence interval for the mean travel time to work.

Note: The standard deviation is large because many people work at home (travel time = 0 minutes) and many have commutes over 1 hour. (Source: Based on data obtained from the American Community Survey.)

5. A schoolteacher is concerned that her students watch more TV than the average American child. She reads that according the to American Academy of Pediatrics (AAP), the average American child in the population watches μ = 4 hours of TV per day. She records the number of hours of TV each of her six (n = 6) students watches per day. The times (in hours) are: 4, 3, 6, 3, 5, and 4. Do these data indicate that her students watch more TV than the average American child in the population?

## Question 2- Z-Critical Values

Conduct the appropriate hypothesis test using α = .05 and state your conclusion in terms of this problem. Make sure to use APA style conclusions (as shown in lecture videos).

6.  Gallagher-Thompson and her colleagues (2001) compared 27 wives who were caring for their spouses who had Alzheimer’s disease to 27 wives who did not have spouses with Alzheimer’s. The two groups of wives were otherwise similar in terms of age, number of years married, and social economic status. The wives were given the Hope Scale (which measures agency and resilience on a scale of 1 to 32) and higher scores indicate more hope. These are the actual data from the study:

 Caregiving Wives Non-caregiving Wives n = 27 n = 27 M = 23.77 M = 26.31 s2 = 4.12 s2 = 6.55

Do these data indicate a significant difference in hope between caregiving and non-caregiving wives?

Conduct the appropriate hypothesis test using α = .01 and state your conclusion in terms of this problem. Make sure to use APA style conclusions (as shown in lecture videos).

7.  Computer and software companies often employ social scientists to research ways their products can better benefit users. For example, Microsoft researchers studied how 15 volunteers performed on a set of tasks under two conditions. The researchers compared the volunteers’ performance on the tasks while using a 15-inch computer monitor and while using a 42-inch monitor (Czerwinski et al., 2003). The 42-inch monitor, far larger than most of us have ever used, allows the user to have multiple programs in view at the same time. The results show an average decrease in time of MD = -11 with s2 = 18.5 when the screen goes from small (15 inches) to large (42 inches).  Does this result support the conclusion that people will perform tasks in a significantly lower amount of time when using a 42-inch monitor than when using a 15-inch monitor?

Conduct the appropriate hypothesis test using α = .05 and state your conclusion in terms of this problem. Make sure to use APA style conclusions (as shown in lecture videos).

8.  Independent or Related (repeated measures) samples? Consider the following studies in which two sets of quantitative measurements were collected. Determine whether the two samples are independent or related.

a.  The effectiveness of a new headache medication is tested by measuring the intensity of a headache in patients before and after drug treatment.

b.  The effectiveness of a new headache medication is tested by measuring the amount of time before the headache is cured for patients who use the new medication and for another group of patients who use a placebo drug.

c.  The accuracy of verbal responses is tested in an experiment in which individuals are first asked to report their height and then their actual height is measured. The data consist of the reported height and the measured height for each individual.

9.  Hypothesis Test? For each of the following scenarios, state which hypothesis test you would use from among the four introduced so far: the z-test, the single-sample t-test, the independent samples t-test, and the related samples t-test.

a.  A study of children who had survived a brain tumor revealed that they were more likely to have behavioral and emotional difficulties than were children who had not experienced such a trauma (Upton & Eiser, 2006). Forty families in which a child had suffered a brain tumor participated in the study. Parents rated children’s difficulties, and the ratings data were compared with known means from published population norms.

b.  In an article titled “A Fair and Balanced Look at the News: What Affects Memory for Controversial Arguments,” Wiley (2005) found that people with a high level of previous knowledge about a given controversial topic (e.g., abortion, military intervention) had better average recall for arguments on both sides of that issue than did those with lower levels of knowledge.

c.  The HOPE VI Panel Study (Popkin & Woodley, 2002) was initiated to test a U.S. program aimed at improving troubled public housing developments. Residents of five HOPE VI developments were examined at the beginning of the study so researchers could later ascertain whether their quality of life had improved. Means at the beginning of the study were compared to known national data sources (e.g., the U.S. Census, the American Housing Survey) that had summary statistics, including means and standard deviations.

d.  Engle-Friedman and colleagues (2003) studied the effects of sleep deprivation. Fifty students were assigned to one night of sleep loss (students were required to call the laboratory every half-hour all night) and then one night of no sleep loss (normal sleep). The next day, students were offered a choice of math problems with differing levels of difficulty. Following the sleep loss, students tended to choose less challenging problems.