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Chapter 7: Q114S (page 387)
A random sample of 175 measurements possessed a mean and a standard deviation s = .79.
a. Test against Use
⦁ The Z-statistic does not fall into the rejection region. So, we fail to reject the
null hypothesis.
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A two-tailed test was conducted with the null and alternative hypotheses stated being \({H_0}:p = .69\) against \({H_a}:p \ne .69\), respectively, with a sample size of 150. The test results were z = -.98 and two-tailed p-value = .327
a. Determine the conditions required for a valid large sample test
Americans’ favorite sport. The Harris Poll (December 2013) conducted an online survey of American adults to determine their favorite sport. Your friend believes professional (National Football League [NFL]) football—with revenue of about $13 billion per year—is the favorite sport for 40% of American adults. Specify the null and alternative hypotheses for testing this belief. Be sure to identify the parameter of interest.
Beta value of a stock. The “beta coefficient” of a stock is a measure of the stock’s volatility (or risk) relative to the market as a whole. Stocks with beta coefficients greater than 1 generally bear the greater risk (more volatility) than the market, whereas stocks with beta coefficients less than 1 are less risky (less volatile) than the overall market (Alexander, Sharpe, and Bailey, Fundamentals of Investments, 2000). A random sample of 15 high-technology stocks was selected at the end of 2009, and the mean and standard deviation of the beta coefficients were calculated: s = .37.
a. Set up the appropriate null and alternative hypotheses to test whether the average high-technology stock is riskier than the market as a whole.
b. Establish the appropriate test statistic and rejection region for the test. Use .
c. What assumptions are necessary to ensure the validity of the test?
d. Calculate the test statistic and state your conclusion.
e. What is the approximate p-value associated with this test? Interpret it.
f. Conduct a test to determine if the variance of the stock beta values differs from .15. Use .
Factors that inhibit learning in marketing. What factors inhibit the learning process in the classroom? To answer this question, researchers at Murray State University surveyed 40 students from a senior-level marketing class (Marketing Education Review). Each student was given a list of factors and asked to rate the extent to which each factor inhibited the learning process in courses offered in their department. A 7-point rating scale was used, where 1 = “not at all” and 7 = “to a great extent.” The factor with the highest rating was instructor related: “Professors who place too much emphasis on a single right answer rather than overall thinking and creative ideas.” Summary statistics for the student ratings of this factor are\(\overline x = 4.70\),\(s = 1.62\)
a. Conduct a test to determine if the true mean rating for this instructor-related factor exceeds 4. Use\(\alpha = 0.05\).Interpret the test results.
b. Examine the results of the study from a practical view, and then discuss why “statistically significant” does not always imply “practically significant.”
c. Because the variable of interest, rating, is measured on a 7-point scale, it is unlikely that the population of ratings will be normally distributed. Consequently, some analysts may perceive the test, part a, to be invalid and search for alternative methods of analysis. Defend or refute this argument
Shopping vehicle and judgment. Refer to the Journal of Marketing Research (December 2011) study of grocery store shoppers’ judgments, Exercise 2.85 (p. 112). For one part of the study, 11 consumers were told to put their arm in a flex position (similar to carrying a shopping basket) and then each consumer was offered several choices between a vice product and a virtue product (e.g., a movie ticket vs. a shopping coupon, pay later with a larger amount vs. pay now). Based on these choices, a vice choice score was determined on a scale of 0 to 100 (where higher scores indicate a greater preference for vice options). The data in the next table are (simulated) choice scores for the 11 consumers. Suppose that the average choice score for consumers with an extended arm position (similar to pushing a shopping cart) is known to be \(\mu = 50\) . The researchers theorize that the mean choice score for consumers shopping with a flexed arm will be higher than 43 (reflecting their higher propensity to select a vice product) Test the theory at \(\alpha = 0.05\)
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