Effectiveness of skin cream. Pond's Age-Defying Complex, a cream with alpha hydroxy acid, advertised that it could reduce wrinkles and improve the skin. In a study published in Archives of Dermatology (June 1996), 33 middle-aged women used a cream with alpha hydroxy acid for 22 weeks. At the end of the study period, a dermatologist judged whether each woman exhibited skin improvement. The results for the 33 women (where $I=$ improved skin and $\mathrm{N}=$ no improvement) are listed in the next table. [Note: Pond's recently discontinued the production of this cream product, replacing it with Age-Defying Towlettes.] Find and interpret the $p$-value of the test.

$\mathrm{I}$	$\mathrm{I}$	$\mathrm{N}$	$\mathrm{I}$	$\mathrm{N}$	$\mathrm{N}$	$\mathrm{I}$	$\mathrm{I}$	$\mathrm{I}$	$\mathrm{I}$	$\mathrm{I}$	$\mathrm{I}$
$\mathrm{N}$	$\mathrm{I}$	$\mathrm{I}$	$\mathrm{I}$	$\mathrm{N}$	$\mathrm{I}$	$\mathrm{I}$	$\mathrm{I}$	$\mathrm{N}$	$\mathrm{I}$	$\mathrm{N}$	$\mathrm{I}$
$\mathrm{I}$	$\mathrm{I}$	$\mathrm{I}$	$\mathrm{I}$	$\mathrm{I}$	$\mathrm{N}$	$\mathrm{I}$	$\mathrm{I}$	$\mathrm{N}$

Refer to the Journal of Marketing Research (Dec. 2011) study of shopping cart design. Design engineers want to know whether you may be more likely to purchase a vice product (e.g., a candy bar) when your arm is flexed (as when carrying a shopping basket) than when your arm is extended (as when pushing a shopping cart). To test this theory, the researchers recruited 22 consumers and had each push their hand against a table while they were asked a series of shopping questions. Half of the consumers were told to put their arm in a flex position (similar to a shopping basket), and the other half were told to put their arm in an extended position (similar to a shopping cart). Participants were offered several choices between a vice and a virtue ( e.g., a movie ticket vs. a shopping coupon, pay later with a larger amount vs. pay now) and a choice score (on a scale of 0 to 100) was determined for each. (Higher scores indicate a greater preference for vice options.) The average choice score for consumers with a flexed arm was 59, while the average for consumers with an extended arm was 43. a. Suppose the standard deviations of the choice scores for the flexed arm and extended arm conditions are 4 and 2, respectively. You were asked whether this information supports the researchers' theory. Now answer the question by conducting a hypothesis test. Use $\alpha=.05$. b. Suppose the standard deviations of the choice scores f or the flexed arm and extended arm conditions are 10 and 15, respectively. You were asked whether this information supports the researchers' theory. Now answer the question by conducting a hypothesis test. Use $\alpha=.05$.

A drug manufacturer claims that fewer than 10% of patients who take its new drug for treating Alzheimer's disease will experience nausea. To test this claim, a significance test is carried out of

$$H_0: p = 0.10$$

$$H_a: p < 0.10$$

You learn that the power of this test at the 5% significance level against the alternative p = 0.08 is 0.29. Explain in simple language what "power = 0.29" means in this setting.

A drug manufacturer claims that less than 10% of patients who take its new drug for treating Alzheimer's disease will experience nausea. To test this claim, researchers conduct an experiment. They give the new drug to a random sample of 300 out of 5000 Alzheimer's patients whose families have given informed consent for the patients to participate in the study. In all, 25 of the subjects experience nausea. Use these data to perform a test of the drug manufacturer's claim at the

$$\alpha = 0.05$$

significance level.

Shopping vehicle and judgment. Refer to the Journal of Marketing Research (December 2011) study of grocery store shoppers' judgments, Exercise $2.85$ (p. 88). 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 $\alpha=.05$.

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 $>0$

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

Junk foods (e.g., potato chips) are typically packaged to appeal to children .. Can similar packaging of a healthy food product influence children's desire to consume the product? This was the question of interest in an article published in the Journal of Consumer Behaviour (Vol. 10, 2011). A fictitious brand of a healthy food product- sliced apples - was packaged to appeal to children (a smiling cartoon apple on the front of the package). The researchers showed the packaging to a sample of 408 schoolchildren and asked each whether he or she was willing to eat the product. Willingness to eat was measured on a 5-point scale, with 1 = "not willing at all" and 5 = "very willing." The data are summarized as follows: $\bar{x}=3.69, s=2.44$. Suppose the researchers know that the mean willingness to eat an actual brand of sliced apples (which is not packaged for children) is $\mu=3$. The data (willingness to eat values) are not normally distributed. How does this affect (if at all) the validity of your conclusion in part a? Explain.

Lobster trap placement. Refer to the Bulletin of Marine Science (April 2010) observational study of lobster trap placement by teams fishing for the red spiny lobster in Baja California Sur, Mexico, Exercise 7.54 (p. 393). Trap-spacing measurements (in meters) for a sample of seven teams of red spiny lobster fishermen are repeated in the table. (These measurements are for the BT cooperative in the accompanying data file.) The researchers want to know whether $\sigma^2$, the variation in the population of trap-spacing measurements, is larger than $10 \mathrm{~m}^2$. They will conduct a test of hypothesis using $\alpha=.05$. Compute the value of the test statistic.

Lobster trap placement. Refer to the Bulletin of Marine Science (April 2010) observational study of lobster trap placement by teams fishing for the red spiny lobster in Baja California Sur, Mexico, Exercise 7.54 (p. 393). Trap-spacing measurements (in meters) for a sample of seven teams of red spiny lobster fishermen are repeated in the table. (These measurements are for the BT cooperative in the accompanying data file.) The researchers want to know whether $\sigma^2$, the variation in the population of trap-spacing measurements, is larger than $10 \mathrm{~m}^2$. They will conduct a test of hypothesis using $\alpha=.05$. Note that $s^2>10$. Consequently, a fisherman wants to reject the null hypothesis. What are the problems with using such a decision rule?

The fiscal year ends December 31 for Lake Hamilton Development. To provide funding for its Moonlight Bay project, LHD issued 5% bonds with a face amount of $500,000 on November 1, 2016. The bonds sold for$442,215, a price to yield the market rate of 6%. The bonds mature October 31, 2036 (20 years). Interest is paid semiannually on April 30 and October 31. Required: 1. What amount of interest expense related to the bonds will LHD report in its income statement for the year ending December 31, 2016? 2. What amount(s) related to the bonds will LHD report in its balance sheet at December 31, 2016? 3. What amount of interest expense related to the bonds will LHD report in its income statement for the year ending December 31, 2017? 4. What amount(s) related to the bonds will LHD report in its balance sheet at December 31, 2017?

Customer participation in store loyalty card programs. Customers who participate in a store's free loyalty card program save money on their purchases but allow the store to keep track of their shopping habits and potentially sell these data to third parties. A Pew Internet & American Life Project Survey (January 2016) revealed that half $(225)$ of a random sample of 250 U.S. adults would agree to participate in a store loyalty card program, despite the potential for information sharing. Explain the theoretical meaning of the phrase, "We are $90 \%$ confident."

Suppose you are interested in conducting the statistical test of

$$H _ { 0 } : \mu = 200 \text { against } H _ { a } : \mu > 200$$

and you have decided to use the following decision rule: Reject

$$H_0$$

if the sample mean of a random sample of 100 items is more than 215. Assume that the standard deviation of the population is 80. a. Express the decision rule in terms of z . b. Find a, the probability of making a Type I error, by using this decision rule.

Relate the nation’s health goals and objectives to individual, family, and community health: Explain why knowing first-aid procedures can help achieve the goals of Healthy People 2010.