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Chapter 7: Q56E (page 417)

Performance of stock screeners. Recall, from Exercise 6.36 (p. 350), that stock screeners are automated tools used by investment companies to help clients select a portfolio of stocks to invest in. The data on the annualized percentage return on investment (as compared to the Standard & Poor鈥檚 500 Index) for 13 randomly selected stock screeners provided by the American Association of Individual Investors (AAII) are repeated in the accompanying table. You want to determine whether \(\mu \) , the average annualized return for all AAII stock screeners, is positive (which implies that the stock screeners perform better, on average, than the S&P 500). An XLSTAT printout of the analysis is shown on the top of page 418.

9.0 -.1 -1.6 14.6 16.0 7.7 19.9 9.8 3.2 24.8 17.6 10.7 9.1

  1. State \({H_0}\,and\,{H_a}\) for this test

Short Answer

Expert verified
  1. \(\begin{aligned}{H_0}:\mu = 0\\{H_a}:\mu > 0\end{aligned}\)

Step by step solution

01

Given Information

The sample size is 13.

\(\mu \) be the average annualized return for screeners.

02

Specifying the null hypothesis

The null hypothesis is given by,

\({H_0}:\mu = 0\)

03

Specifying the alternative hypothesis

The alternative hypothesis is given by,

\({H_a}:\mu > 0\)

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Most popular questions from this chapter

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.

A random sample of 41 observations from a normal population possessed a mean \(\bar x = 88\) and a standard deviation s = 6.9.

a. Test \({H_0}:{\sigma ^2} = 30\) against \({H_a}:{\sigma ^2} > 30\). Use\(\alpha = 0.05.\)

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 = 鈥渘ot at all鈥� and 7 = 鈥渢o a great extent.鈥� The factor with the highest rating was instructor related: 鈥淧rofessors who place too much emphasis on a single right answer rather than overall thinking and creative ideas.鈥� 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 鈥渟tatistically significant鈥� does not always imply 鈥減ractically significant.鈥�

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

For each of the following rejection regions, sketch the sampling distribution for z and indicate the location of the rejection region.

a. \({H_0}:\mu \le {\mu _0}\) and \({H_a}:\mu > {\mu _0};\alpha = 0.1\)

b. \({H_0}:\mu \le {\mu _0}\) and \({H_a}:\mu > {\mu _0};\alpha = 0.05\)

c. \({H_0}:\mu \ge {\mu _0}\) and \({H_a}:\mu < {\mu _0};\alpha = 0.01\)

d. \({H_0}:\mu = {\mu _0}\) and \({H_a}:\mu \ne {\mu _0};\alpha = 0.05\)

e. \({H_0}:\mu = {\mu _0}\) and \({H_a}:\mu \ne {\mu _0};\alpha = 0.1\)

f. \({H_0}:\mu = {\mu _0}\) and \({H_a}:\mu \ne {\mu _0};\alpha = 0.01\)

g. For each rejection region specified in parts a鈥揻, state the probability notation in z and its respective Type I error value.

A border protection avatar. The National Center for Border Security and Protection has developed the "Embodied Avatar"鈥攁 kiosk with a computer-animated border guard that uses artificial intelligence to scan passports, check fingerprints, read eye pupils, and asks questions of travellers crossing the U.S. border. (National Defense Magazine, February 2014.) Based on field tests, the avatar's developer claims that the avatar can detect deceitful speech correctly 75% of the time.

a. Identify the parameter of interest.

b. Give the null and alternative hypotheses for testing the claim made by the avatar's developer.

c. Describe a Type I error in the words of the problem.

d. Describe a Type II error in the words of the problem
See all solutions

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