The most common injury that occurs among mountain climbers is trauma to the lower extremity (leg). Consequently, rescuers must be proficient in immobilizing and splinting of fractures. In High Altitude Medicine & Biology (Vol. 10, 2009), researchers provided official recommendations for mountain emergency medicine. As part of the document, the researchers examined the likelihood of needing certain types of splints. A Scottish Mountain Rescue study reported that there was 1 femoral shaft splint needed among 333 live casualties. The researchers will use this study to estimate the proportion of all mountain casualties that require a femoral shaft splint. Is the sample large enough to apply the large-sample estimation method of this section? Show why or why not.

Use a percent proportion to find each percentage. 5% of 74

Describe emergency care for stroke.

Solve the differential equation.

$$\sec x\ d y + x \cos ^ { 2 } y\ d x = 0$$

Refer to the international Conference on Social Robotics (Vol. 6414, 2010) study of the trend in the design of social robots. The researchers obtained a random sample of 106 social robots through a Web search and determined the number that were designed with legs, but no wheels. Let $\hat{p}$ represent the sample proportion of social robots designed with legs, but no wheels. Assume that in the population of all social robots, 40% are designed with legs, but no wheels. Give the mean and standard deviation of the sampling distribution of $\hat{p}$.

Evaluate each of the following. a) P(7,2) b) P(8, 4) c) P(10, 7) d) P(12, 3)

For the binomial sample information summarized in each part, indicate whether the sample size is large enough to use the methods of this chapter to construct a confidence interval for p .

$$\begin{array} { l } { \text { a. } n = 500 , \hat { p } = .05 } \\ { \text { b. } n = 100 , \hat { p } = .05 } \\ { \text { c. } n = 10 , \hat { p } = .5 } \\ { \text { d. } n = 10 , \hat { p } = .3 } \end{array}$$

Explain why a "standardized statistic" is used in hypothesis testing, instead of simply using the difference between the sample statistic and the null value as the test statistic.

What is meant by the term "90% confident" when constructing a confidence interval for a mean?

a. If we took repeated samples, approximately $90 \%$ of the samples would produce the same confidence interval.

b. If we took repeated samples, approximately $90 \%$ of the confidence intervals calculated from those samples would contain the sample mean.

c. If we took repeated samples, approximately $90 \%$ of the confidence intervals calculated from those samples would contain the true value of the population mean.

d. If we took repeated samples, the sample mean would equal the population means in approximately $90 \%$ of the samples.

Describe the sampling distribution of

$$\hat { p }$$

on the basis of large samples of size n . That is, give the mean, the standard deviation, and the (approximate) shape of the distribution of

$$\hat { p }$$

when large samples of size n are (repeatedly) selected from the binomial distribution with probability p of success.

Why do the Gauls fear the Druids?

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.

Sketch the atomic structure of silicon and insert an impurity of indium.

In each case, find the approximate sample size required to construct a 95% confidence interval for p that has sampling error SE = .06. a. Assume that p is near .3. b. Assume that you have no prior knowledge about p , but you wish to be certain that your sample is large enough to achieve the specified accuracy for the estimate.