Consider each of these situations. Do you think the proposed sampling method is appropriate? Explain. We want to know if there is neighborhood support to turn a vacant Jot into a playground. We spend a Saturday afternoon going door-to-door in the neighborhood, asking people to sign a petition.

Researchers conducted a study to determine whether magnets are effective in treating back pain, with results given below (based on data from "Bipolar Permanent Magnets for the Treatment of Chronic Lower Back Pain: A Pilot Study," by ColJacott, Zimmerman, White, and Rindone, Journal of the American Medical Association, Vol. 283, No. IO). The values represent measurements of pain using the visual analog scale. Use a 0.05 significance level to test the claim that those given a sham treatment (similar to a placebo) have pain reductions that vary more than the pain reductions for those treated with magnets.

$$\begin{aligned} \text { Reduction in Pain Level After Sham Treatment: } & n = 20 , \overline { x } = 0.44 , s = 1.4 \\ \text { Reduction in Pain Level After Magnet Treatment: } & n = 20 , \overline { x } = 0.49 , s = 0.96 \end{aligned}$$

An elementary school teacher with 25 students plans to have each of them make a poster about two different states. The teacher first numbers the states (in alphabetical order, from I-Alabama to SO-Wyoming), then uses a random number table to decide which states each student gets. Here are the random digits: 45921 01710 22892 37076 a) Which two state numbers does the first student get b) Which two state numbers go to the second student?

Consider this situation. Do you think the proposed sampling method is appropriate? Explain. We want to know what percentage of local doctors accept Medicaid patients. We call the offices of 50 doctors randomly selected from local Yellow Page listings.

Concerned about reports of discolored scales on fish caught downstream from a newly sited chemical plant, scientists set up a field station in a shoreline public park. For one week, they asked fishermen there to bring any fish they caught to the field station for a brief inspection. At the end of the week, the scientists said that 18% of the 234 fish that were submitted for inspection displayed the discoloration. From this information, can the researchers estimate what proportion of fish in the river have discolored scales? Explain.

Consider each of these situations. Do you think the proposed sampling method is appropriate? Explain. a) We want to know if there is neighborhood support to turn a vacant lot into a playground. We spend a Saturday afternoon going door to door in the neighborhood, asking people to sign a petition. b) We want to know if students at our college are satisfied with the selection of food available on campus. We go to the largest cafeteria and interview every 10th person in line.

Consider each of these situations. Do you think the proposed sampling method is appropriate? Explain.

We want to know if there is neighborhood support to turn a vacant lot into a playground. We spend a Saturday afternoon going door-to-door in the neighborhood, asking people to sign a petition.

A lot acceptance sampling plan for large lots specifies that 50 items be randomly selected and that the lot be accepted if no more than 5 of the items selected do not conform to specifications. What is the approximate probability that a lot will be accepted if the true proportion of nonconforming items in the lot is .10?

Refer to Exercise 9.3. Compute the mean and standard deviation of the simulated sampling distribution. Compare them with the theoretical values of $\mu_{\bar{x}}$ and $\sigma_{\bar{x}}$, which are:

$$\mu_{\bar{x}}=\mu=3.5$$

$$\sigma_{\bar{x}}=\frac{\sigma}{\sqrt{n}}=\frac{1.71}{\sqrt{10}}=.54$$

Suppose that 47% of all adult women think they do not get enough time for themselves. An opinion poll interviews 1025 randomly chosen women and records the sample proportion who feel they don't get enough time for themselves. Describe the sampling distribution

$$\hat{p}$$

.

Suppose a large candy machine has 15% orange candies. Imagine taking an SRS of 25 candies from the machine and observing the sample proportion

$$\hat{p}$$

of orange candies. Find the standard deviation of the sampling distribution of

$$\hat{p}.$$

Check to see if the 10% condition is met.

You see a female student standing in front of the cafeteria, now and then stopping other students to ask them questions. She says that she is conducting a survey of student opinions about the quality of food in the cafeteria. Explain why this sampling method is almost certainly biased.

What is the age of the surface bedrock throughout most of the Finger Lakes region of New York State? (1) Cambrian (2) Devonian (3) Pennsylvanian (4) Permian

Let x be a random variable representing the amount of sleep each adult in New York City got last night. Consider a sampling distribution of sample means $\bar{x}$. As the sample size becomes increasingly large, what value will the mean $\mu_{x}$ of the $\bar{x}$ distribution approach?