Chapter 7: Q7E (page 397)
If you test a hypothesis and reject the null hypothesis in favor of the alternative hypothesis, does your test prove that the alternative hypothesis is correct? Explain.
Saying that a test proves the alternative is correct is an inaccurate statement.
Over 30 million students worldwide already upgrade their learning with Vaia!
All the tools & learning materials you need for study success - in one app.
Get started for free
Hotels’ use of ecolabels. Refer to the Journal of Vacation Marketing (January 2016) study of travelers’ familiarity with ecolabels used by hotels, Exercise 2.64 (p. 104). Recall that adult travelers were shown a list of 6 different ecolabels, and asked, “Suppose the response is measured on a continuous scale from 10 (not familiar at all) to 50 (very familiar).” The mean and standard deviation for the Energy Star ecolabel are 44 and 1.5, respectively. Assume the distribution of the responses is approximately normally distributed.
a. Find the probability that a response to Energy Star exceeds 43.
b. Find the probability that a response to Energy Star falls between 42 and 45. c. If you observe a response of 35 to an ecolabel, do you think it is likely that the ecolabel was Energy Star? Explain.
Question: Point spreads of NFL games. Refer to the Chance (Fall 1998) study of point-spread errors in NFL games, Exercise 7.41 (p. 411). Recall that the difference between the actual game outcome and the point spread established by odds makers—the point-spread error—was calculated for 240 NFL games. The results are summarized as follows: . Suppose the researcher wants to know whether the true standard deviation of the point spread errors exceeds 15. Conduct the analysis using α = 0.10.
Time required to complete a task. When a person is asked, “How much time will you require to complete this task?” cognitive theory posits that people (e.g., a business consultant) will typically underestimate the time required. Would the opposite theory hold if the question was phrased in terms of how much work could be completed in a given amount of time? This was the question of interest to researchers writing in Applied Cognitive Psychology (Vol. 25, 2011). For one study conducted by the researchers, each in a sample of 40 University of Oslo students was asked how many minutes it would take to read a 32-page report. In a second study, 42 students were asked how many pages of a lengthy report they could read in 48 minutes. (The students in either study did not actually read the report.) Numerical descriptive statistics (based on summary information published in the article) for both studies are provided in the accompanying table.
a. The researchers determined that the actual mean time it takes to read the report in\(\mu = 48\) minutes. Is there evidence to support the theory that the students, on average, overestimated the time it would take to read the report? Test using\(\alpha = 0.10\).
b. The researchers also determined that the actual mean number of pages of the report that is read within the allotted time is\(\mu = 32\)pages. Is there evidence to support the theory that the students, on average, underestimated the number of report pages that could be read? Test using\(\alpha = 0.10\)
c. The researchers noted that the distribution of both estimated time and number of pages is highly skewed (i.e., not normally distributed). Does this fact impact the inferences derived in parts a and b? Explain.
7.83 A random sample of n observations is selected from a normal population to test the null hypothesis that . Specify the rejection region for each of the following combinations of and .
a.
b.
c.
d.
e.
f.
For each of the following situations, determine the p-value and make the appropriate conclusion.
a.\({H_0}:\mu \le 25\),\({H_a}:\mu > 25\),\(\alpha = 0.01\),\(z = 2.02\)
b.\({H_0}:\mu \ge 6\),\({H_a}:\mu < 6\),\(\alpha = 0.05\),\(z = - 1.78\)
c.\({H_0}:\mu = 110\),\({H_a}:\mu \ne 110\),\(\alpha = 0.1\),\(z = - 1.93\)
d. \({H_0}:\mu = 10\), \({H_a}:\mu \ne 10\), \(\alpha = 0.05\), \(z = 1.96\)
What do you think about this solution?
We value your feedback to improve our textbook solutions.
