Unethical corporate conduct. Refer to the Behavioral Research in Accounting (July 2015) study of unethical corporate conduct, Exercise $6.15$ (p. 316). Recall that each in a sample of 86 accounting graduate students was asked to perform an unethical task (e.g., to bribe a customer), and each subject's intention to comply with the unethical request score was measured. [Scores ranged from $-1.5$ (intention to resist the unethical request) to $2.5$ (intention to comply with the unethical request)]. Summary statistics on the 86 scores follow: $\bar{x}=2.42, s=2.84$. One researcher, of the opinion that subjects will tend to perform the unethical task, believes the population mean intention score $\mu$ will exceed 2. Do the data support this belief? Test using $\alpha=.01$

Trading skills of institutional investors. The trading skills of institutional stock investors were quantified and analyzed in The Journal of Finance (April 2011). The study focused on "round-trip" trades, i.e., trades in which the same stock was both bought and sold in the same quarter. Consider a random sample of 200 round-trip trades made by institutional investors. Suppose the sample mean rate of return is $2.95 \%$ and the sample standard deviation is $8.82 \%$. If the true mean rate of return of round-trip trades is positive, then the population of institutional investors is considered to have performed successfully. Interpret the value of $\alpha$ in the words of the problem. Test of $\mu=0$ va $>0$

$$\begin{array}{rrrrrrrr}\mathrm{N} & \text { Mean } & \text { StDev } & \text { SE Mean } & \text { M5 Lower Bound } & 7 & \text { Dow } \\ 200 & 2.950 & \text { B.820 } & 0.624 & & 1.919 & 4.73 & 0.000\end{array}$$

Trading skills of institutional investors. The trading skills of institutional stock investors were quantified and analyzed in The Journal of Finance (April 2011). The study focused on "round-trip" trades, i.e., trades in which the same stock was both bought and sold in the same quarter. Consider a random sample of 200 round-trip trades made by institutional investors. Suppose the sample mean rate of return is $2.95 \%$ and the sample standard deviation is $8.82 \%$. If the true mean rate of return of round-trip trades is positive, then the population of institutional investors is considered to have performed successfully. Give the appropriate conclusion in the words of the problem. Test of $\mu=0$ va $>0$

$$\begin{array}{rrrrrrrr}\mathrm{N} & \text { Mean } & \text { StDev } & \text { SE Mean } & \text { M5 Lower Bound } & 7 & \text { Dow } \\ 200 & 2.950 & \text { B.820 } & 0.624 & & 1.919 & 4.73 & 0.000\end{array}$$

A random sample of 100 observations from a population with standard deviation 60 yielded a sample mean of 110. Test the null hypothesis that

$$\mu = 100$$

against the alternative hypothesis that

$$\mu > 100 , \text { using } \alpha = .05$$

Interpret the results of the test.

Stability of compounds in new drugs. Refer to the ACS Medicinal Chemistry Letters (Vol. 1, 2010) study of the metabolic stability of drugs, Exercise $2.22$ (p. 59). Recall that two important values computed from the testing phase are the fraction of compound unbound to plasma (fup) and the fraction of compound unbound to microsomes (fumic). A key formula for assessing stability assumes that the fup/fumic ratio is 1:1. Pharmacologists at Pfizer Global Research and Development tested 416 drugs and reported the fup/fumic ratio for each. These data are saved in the FUP file, and summary statistics are provided in the accompanying Minitab printout. Suppose the pharmacologists want to determine if the true mean ratio, $\mu$, differs from 1. Give the appropriate conclusion, based on the results of parts $\mathbf{c}$ and $\mathbf{d}$.

In a test of

$$H _ { 0 } : \mu = 100 \text { against } H _ { a } : \mu \neq 100$$

the sample data yielded the test statistic z = 2.17. Find the p -value for the test.

Refer to the Business and Society (Mar. 2011) study on the sustainability behaviors of CPA corporations. Recall that corporate sustainability refers to business practices designed around social and environmental considerations. The level of support senior managers have for corporate sustainability was measured quantitatively on a scale ranging from 0 to 160 points, where higher point values indicate a higher level of support for sustainability. The study provided the following information on the distribution of levels of support for sustainability: $\mu=68, \sigma=27$. Now consider a random sample of 30 senior managers and let $\bar{x}$ represent the sample mean level of support. Find $P(\bar{x}>65)$.

Refer to the Business and Society (Mar. 2011) study on the sustainability behaviors of CPA corporations. Recall that the level of support for corporate sustainability (measured on a quantitative scale ranging from 0 to 160 points) was obtained for each in a sample of 992 senior managers at CPA firms. The data (where higher point values indicate a higher level of support for sustainability) are saved in the referenced file. The CEO of a CPA firm claims that the true mean level of support for sustainability is 75 points. Specify the null and alternative hypotheses for testing this claim. One Sample Statistics $$ \begin{matrix} \text{ } & \text{N} & \text{Mean} & \text{Std. Deviation} & \text{Std. Error Mean}\\ \text{SUPPORT} & \text{992} & \text{67.76} & \text{26.871} & \text{.853}\\ \end{matrix} $$ One sample Test. Test Value = 75. $$ \begin{matrix} \text{ } & \text{t} & \text{df} & \text{Sig. (2-talled)} & \text{Mean Dífference} & \text{95\\% Contidence lnterval of the Difference}\\ \text{SUPPORT} & \text{-8.492} & \text{991} & \text{.000} & \text{-7.245} & \text{Lower -8.92} & \text{Upper -5.57}\\ \end{matrix} $$

The Professional Golf Association (PGA) and Golf Digest have developed the Play Golf America program, in which teaching professionals at participating golf clubs provide a free 10-minute lesson to new customers. According to Golf Digest (July 2008), golf facilities that participate in the program gain, on average, $2,400 in green fees, lessons, or equipment expenditures. A teaching professional at a golf club believes that the average gain in green fees, lessons, or equipment expenditures for participating golf facilities exceeds$2,400. In order to support the claim made by the teaching professional, what null and alternative hypothesis should you test?

In a test of the hypothesis

$$H _ { 0 } : \mu = 10 \text { versus } H _ { a } : \mu \neq 10$$

a sample of n = 50 observations possessed mean

$$\overline { x } = 10.7$$

and standard deviation s = 3.1. Find and interpret the p -value for this test.

For each pair consisting of a and an observed significance level (p -value), indicate whether the null hypothesis would be rejected.

$$\alpha = .05 , p -value = .10$$

Consider the test $H_0: \mu=70$ versus $H_{\mathrm{a}}: \mu>70$ using a large sample of size $n=400$. Assume $\sigma=20$. Describe the sampling distribution of $\bar{x}$.

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

$$z > 1.96$$

What is the difference between Type I and Type II errors in hypothesis testing? How do a and b relate to Type I and Type II errors?