91Ó°ÊÓ

\(A\) club has 30 student members and 10 faculty members. The students are $$ \begin{array}{lllll} \hline \text { Abel } & \text { Fisher } & \text { Huber } & \text { Miranda } & \text { Reinmann } \\ \text { Carson } & \text { Ghosh } & \text { Jimenez } & \text { Moskowitz } & \text { Santos } \\ \text { Chen } & \text { Griswold } & \text { Jones } & \text { Neyman } & \text { Shaw } \\ \text { David } & \text { Hein } & \text { Kim } & \text { 0'Brien } & \text { Thompson } \\ \text { Deming } & \text { Hernandez } & \text { Klotz } & \text { Pearl } & \text { Utts } \\ \text { Elashoff } & \text { Holland } & \text { Liu } & \text { Potter } & \text { Varga } \\ \hline \end{array} $$ $$ \text { The faculty members are } $$ $$ \begin{array}{lllll} \hline \text { Andrews } & \text { Fernandez } & \text { Kim } & \text { Moore } & \text { West } \\ \text { Besicovitch } & \text { Gupta } & \text { Lightman } & \text { Phillips } & \text { Yang } \\ \hline \end{array} $$ The club can send 4 students and 2 faculty members to a convention. It decides to choose those who will go by random selection. Describe a method for using Table \(\mathrm{D}\) to select a stratified random sample of 4 students and 2 faculty. Then use line 123 to select the sample.

Michigan Stadium, also known as "The Big House," seats over 100,000 fans for a football game. The University of Michigan athletic department plans to conduct a survey about concessions that are sold during games. Tickets are most expensive for seats on the sidelines. The cheapest seats are in the end zones (where one of the authors sat as a student). A map of the stadium is shown. (a) The athletic department is considering a stratified random sample. What would you recommend as the strata? Why? (b) Explain why a cluster sample might be easier to obtain. What would you recommend for the clusters? Why?

A lumber company wants to estimate the proportion of trees in a large forest that are ready to be cut down. They use an aerial map to divide the forest into 200 equal-sized rectangles. Then they choose a random sample of 20 rectangles and examine every tree that's in one of those rectangles. (a) What is the name for this kind of sampling method? (b) Give a possible reason why the lumber company chose this method.

What proportion of students at your school use Twitter? To find out, you survey a simple random sample of students from the school roster. (a) Will your sample result be exactly the same as the true population proportion? Explain. (b) Which would be more likely to get your sample result closer to the true population value: an SRS of 50 students or an SRS of 100 students? Explain.

A common form of nonresponse in telephone surveys is "ring-no-answer." That is, a call is made to an active number but no one answers. The Italian National Statistical Institute looked at nonresponse to a government survey of households in Italy during the periods January 1 to Easter and July 1 to August \(31 .\) All calls were made between 7 and \(10 \mathrm{p} \cdot \mathrm{M} .,\) but \(21.4 \%\) gave "ring-no-answer" in one period versus \(41.5 \%\) "ring-no-answer" in the other period. \({ }^{16}\) Which period do you think had the higher rate of no answers? Why? Explain why a high rate of nonresponse makes sample results less reliable.

A biologist would like to determine which of two brands of weed killer, X or \(Y\), is less likely to harm the plants in a garden at the university. Before spraying near the plants, the biologist decides to conduct an experiment using 24 individual plants. Which of the following two plans for randomly assigning the treatments should the biologist use? Why? Plan A: Choose the 12 healthiest-looking plants. Then flip a coin. If it lands heads, apply Brand X weed killer to these plants and Brand Y weed killer to the remaining 12 plants. If it lands tails, do the opposite. Plan B: Choose 12 of the 24 plants at random. Apply Brand X weed killer to those 12 plants and Brand \(Y\) weed killer to the remaining 12 plants.

As men age, their testosterone levels gradually decrease. This may cause a reduction in lean body mass, an increase in fat, and other undesirable changes. Do testosterone supplements reverse some of these effects? A study in the Netherlands assigned 237 men aged 60 to 80 with low or low-normal testosterone levels to either a testosterone supplement or a placebo. The report in the Journal of the American Medical Association described the study as a "double-blind, randomized, placebo-controlled trial." Explain each of these terms to someone who knows nothing about statistics.

To investigate whether standing up while studying affects performance in an algebra class, a teacher assigns half of the 30 students in his class to stand up while studying and assigns the other half to not stand up while studying. To determine who receives which treatment, the teacher identifies the two students who did best on the last exam and randomly assigns one to stand and one to not stand. The teacher does the same for the next two highest-scoring students and continues in this manner until each student is assigned a treatment. Which of the following best describes this plan? (a) This is an observational study. (b) This is an experiment with blocking. (c) This is a completely randomized experiment. (d) This is a stratified random sample. (e) This is a cluster sample.

A gardener wants to try different combinations of fertilizer (none, 1 cup, 2 cups) and mulch (none, wood chips, pine needles, plastic) to determine which combination produces the highest yield for a variety of green beans. He has 60 green-bean plants to use in the experiment. If he wants an equal number of plants to be assigned to each treatment, how many plants will be assigned to each treatment? (a) 1 (b) 3 (c) 4 (d) 5 (e) 12

Explain the difference between the types of inference than can usually be made from an observational study and an experiment.