The likelihood that a person with a contagious disease will infect others in a social situation may be assumed to be a function $f(s)$ of the distance $s$ between individuals. Suppose contagious individuals are uniformly distributed throughout a rectangular region $R$ in the $x y$ plane. Then the likelihood of infection for someone at the origin $(0,0)$ is proportional to the exposure index $E$, given by the double integral

$$E=\iint_R f(s) d A$$

where $s=\sqrt{x^2+y^2}$ is the distance between $(0,0)$ and $(x, y)$. Find $E$ for the case where

$$f(s)=1-\frac{s^2}{9}$$

and $R$ is the square

$$R:-2 \leq x \leq 2,-2 \leq y \leq 2$$

The U.S. Center for Disease Control reports that the mean life expectancy was $47.6$ years for whites born in 1900 and $33.0$ years for nonwhites. Suppose that you randomly survey death records for people born in 1900 in a certain county. Of the 124 whites, the mean life span was $45.3$ years with a standard deviation of $12.7$ years. Of the 82 nonwhites, the mean life span was $34.1$ years with a standard deviation of $15.6$ years. Conduct a hypothesis test to see if the mean life spans in the county were the same for whites and nonwhites.

State the null and alternative hypotheses.

$H_a$ :

The sentence in this exercise contains an italicized word beginning with circum- or peri-. The root word and its meaning are given in parentheses after the sentence. Step 1: Taking the context into consideration, write your own definition of the word. Step 2: Write the dictionary definition of the word. Choose the definition that fits the way in which the word is used in the sentence. Step 3: Write a sentence of your own in which you use the word correctly.

Good dental hygiene helps to prevent periodontal disease. (Latin root word: dentis, "of a tooth")

YOUR DEFINITION ____________________________________________________________________________________________________________________

DICTIONARY DEFINITION ____________________________________________________________________________________________________________________

SENTENCE ____________________________________________________________________________________________________________________

Here are the survival times in days of 72 guinea pigs after they were injected with infectious bacteria in a medical experiment. Survival times usually have distributions that are skewed to the right.

$$\begin{array}{llllllllllll}43 & 45 & 53 & 56 & 56 & 57 & 58 & 66 & 67 & 73 & 74 & 79 \\ 80 & 80 & 81 & 81 & 81 & 82 & 83 & 83 & 84 & 88 & 89 & 91 \\ 91 & 92 & 92 & 97 & 99 & 99 & 100 & 100 & 101 & 102 & 102 & 102 \\ 103 & 104 & 107 & 108 & 109 & 113 & 114 & 118 & 121 & 123 & 126 & 128 \\ 137 & 138 & 139 & 144 & 145 & 147 & 156 & 162 & 174 & 178 & 179 & 184 \\ 191 & 198 & 211 & 214 & 243 & 249 & 329 & 380 & 403 & 511 & 522 & 598 \end{array}$$

Which measure of center and spread would you use to summarize the distribution-the mean and standard deviation or the median and IQR? Justify your answer.

Beef Consumption. Many medical professionals believe that eating too much red meat increases the risk of heart disease and cancer. Suppose you would like to conduct a survey to determine the yearly consumption of beef by a typical American and want to use 3 pounds as the desired margin of error for a confidence interval estimate of the population mean amount of beef consumed annually. Use 25 pounds as a planning value for the population standard deviation and recommend a sample size for each of the following situations.

b. A $95 \%$ confidence interval is desired for the mean amount of beef consumed.

The U.S. Center for Disease Control reports that the mean life expectancy was $47.6$ years for whites born in 1900 and $33.0$ years for nonwhites. Suppose that you randomly survey death records for people born in 1900 in a certain county. Of the 124 whites, the mean life span was $45.3$ years with a standard deviation of $12.7$ years. Of the 82 nonwhites, the mean life span was $34.1$ years with a standard deviation of $15.6$ years. Conduct a hypothesis test to see if the mean life spans in the county were the same for whites and nonwhites.

State the null and alternative hypotheses.

$H_a$ : $\rule{1cm}{1pt}$

In a test for toxemia, a disease that affects pregnant women, a woman lies on her left side and then rolls over on her back. The test is considered positive if there is a 20-mm rise in her blood pressure within 1 minute. The results have produced the following probabilities, where T represents having toxemia at some time during the pregnancy and N represents a negative test:

$$P\left(T^{\prime} \mid N\right)=.90 \text { and } P\left(T \mid N^{\prime}\right)=.75 .$$

Assume that $P\left(N^{\prime}\right)=.11$, and find each of the given probabilities.

$$P\left(N^{\prime} \mid T\right)$$

The following table shows data on average per capita wine consumption and heart disease rate in a random sample of 10 countries. a. Enter the data into your calculator and make a scatter plot. b. Use your calculator’s regression function to find the equation of the least-squares regression line. Add this to your scatter plot from part a. c. Explain in words what the slope and y-intercept of the regression line tell us. d. How well does the regression line fit the data? Explain your response. e. Which point has the largest residual? Explain what the residual means in context. Is this point an outlier? An influential point? Explain. f. Do the data provide convincing evidence that there is a linear relationship between the amount of alcohol consumed and the heart disease death rate? Carry out an appropriate test at a significance level of 0.05 to help answer this question.

$$\begin{matrix} \text{Yearly wine consumption in liters} & \text{2.5} & \text{ 3.9} & \text{2.9} & \text{2.4} & \text{2.9} & \text{0.8} & \text{9.1} & \text{ 2.7} & \text{0.8} & \text{ 0.7}\\ \text{Death from heart diseases} & \text{221} & \text{167} & \text{131} & \text{191} & \text{220} & \text{297} & \text{71} & \text{172} & \text{211} & \text{300}\\ \text{Table 12.25}\\ \end{matrix}$$

In 1990, the mean height of women 20 years of age or older was 63.7 inches based on data obtained from the Centers for Disease Control and Prevention's Advance Data Report. Suppose that a random sample of 45 women who are 20 years of age or older today results in a mean height of 63.9 inches. (a) State the appropriate null and alternative hypotheses to assess whether women are taller today. (b) Suppose the P-value for this test is 0.35. Exp lain what this value represents. (c) Write a conclusion for this hypothesis test assuming an $\alpha$=0.10 level of significance.

The U.S. Center for Disease Control reports that the mean life expectancy was $47.6$ years for whites born in 1900 and $33.0$ years for nonwhites. Suppose that you randomly survey death records for people born in 1900 in a certain county. Of the 124 whites, the mean life span was $45.3$ years with a standard deviation of $12.7$ years. Of the 82 nonwhites, the mean life span was $34.1$ years with a standard deviation of $15.6$ years. Conduct a hypothesis test to see if the mean life spans in the county were the same for whites and nonwhites.

At a pre-conceived $\alpha=0.05$, what is your:

Reason for the decision:

Approximately 3.6% of all (untreated) Jonathan apples had bitter pit in a study conducted by the botanists Ratkowsky and Martin. (Bitter pit is a disease of apples resulting in a soggy core, which can be caused either by overwatering the apple tree or by a calcium deficiency in the soil.) Let n be a random variable that represents the first Jonathan apple chosen at random that has bitter pit. Write out a formula for the probability distribution of the random variable n. What is the expected number of apples that must be examined to find the first one with bitter pit? Hint: Use $\mu$ for the geometric distribution and round.

Which statement best describes an interaction between the circulatory and respiratory systems that helps maintain homeostasis? (A) Blood plasma transports salts, sugars, fats, and dissolved proteins through the body to keep it healthy. (B) The diaphragm and rib cage work together to move air into and out of the lungs. (C) The lymphatic system contains nodes that act as filters to remove bacteria that could otherwise cause disease. (D) Blood cells pick up and carry oxygen from the lungs to the body cells. (E) T he lymphatic system collects and returns fluid that leaks from blood vessel.

Ms. W.P. is 42 years old and has had rheumatoid arthritis for 6 years. Her fingers are stiff and show slight ulnar deviation. She is now experiencing an exacerbation, and her wrists are red and swollen. She finds it to be painful when something such as clothing touches the skin over her wrists. Her elbows and knees are also stiff and painful, especially after she has been resting. She is feeling extremely tired and depressed and has not been eating well. Predict the possible course of this disease in Ms. W.P.

Indicate whether each of the following statements relating to trans fatty acids is true or false.

a. Partial hydrogenation processes involving triacylglycerols effect the conversion of some cis double bonds to single bonds.

b. Partial hydrogenation processes involving triacylglycerols effect the conversion of some single bonds to trans double bonds.

c. Biochemically, trans fatty acids and saturated fatty acids have similar effects relative to cardiovascular disease.

d. The degree of carbon-chain bending is greater for trans fatty acids than cis fatty acids.