Population Statistics The table shows the life expectancy of a child (at birth) in the United States for selected years from 1920 to 2000. (Source: U.S. National Center for Health Statistics, U.S. Census Bureau)

$$\begin{array}{|c|c|} \hline \text { Year, } t & \text { Life expectancy, } y \\ \hline 1920 & 54.1 \\ 1930 & 59.7 \\ 1940 & 62.9 \\ 1950 & 68.2 \\ 1960 & 69.7 \\ 1970 & 70.8 \\ 1980 & 73.7 \\ 1990 & 75.4 \\ 2000 & 77.1 \\ \hline \end{array}$$

A model for the life expectancy during this period is

$$y=-0.0025 t^2+0.572 t+44.31$$

where $y$ represents the life expectancy and $t$ is the time in years, with $t=20$ corresponding to 1920 .

Use the graph of the model to estimate the life expectancy of a child for the years 2005 and 2010.

Joe is writing a report on the backgrounds of American presidents. He looks up information on how many of the 44 presidents were only children. Because Joe took a statistics course, he uses these results to get a $95\%$ confidence interval for the true proportion p of these 44 U.S. presidents who were only children. This makes no sense. Why not?

By using the Bureau of Labor Statistics inflation calculator to complete the following sentence. Round your answer to the nearest dollar. Note: If the calculator asks you to choose a month, choose January. Suppose that $Y$ is the year in which you were born and that $\$ C$ today is worth $\$ D$ in year $Y$. Is $C$ greater than or less than $D$?

A small company involved in e-commerce is interested in statistics concerning the use of e-mail. A poll encountered that $38 \%$ of a random sample of 1012 adults, who use a computer at their home, work, or school, said that they do not send or receive e-mail.

c) If we want to be $99 \%$ confident, will the margin of error be larger or smaller? Describe.

Perform each of the following steps.

a. State the hypotheses and identify the claim. b. Find the critical value(s). c. Find the test value. d. Make the decision. e. Summarize the results.

Use the traditional method of hypothesis testing unless otherwise specified.

According to the Bureau of Transportation Statistics, on-time performance by airlines is described as follows:

Records of 200 randomly selected flights for a major airline company showed that 125 planes were on time; 40 were delayed because of weather, 10 because of a National Aviation System delay, and the rest because of arriving late. At $\alpha=0.05$, do these results differ from the government's statistics?

Use the following data set. The data represent the heights (in inches) of students in a statistics class.

$$\begin{array}{llllllllll}52 & 54 & 55 & 56 & 56 & 56 & 58 & 59 & 60 & 61 \\ 61 & 63 & 65 & 67 & 68 & 68 & 70 & 71 & 72 & \end{array}$$

Find the height that corresponds to the first quartile.

Using the simple random sample of weights of women from the mentioned data set, we obtain these sample statistics: $n=40$ and $\bar{x}=146.22$ lb. Research from other sources suggests that the population of weights of women has a standard deviation given by $\sigma=$30.86 lb.

a. Find the best point estimate of the mean weight of all women.

A Statistics professor has observed that for several years students score an average of 105 points out of 150 on the semester exam. A sales man suggests that he try a statistics software package that gets students more involved with computers, predicting that it will increase students' scores. The software is expensive, and the salesman offers to let the professor use it for a semester to see if the scores on the final exam increase significantly. The professor will have to pay for the software only if he chooses to continue using it. a) Is this a one-tailed or two-tailed test ? Explain. b) Write the null and alternative hypotheses. c) In this context, explain what would happen if the professor makes a Type I error. d) In this context, explain what would happen if the professor make s a Type II error. e) What is meant by the power of this test?

Find the Maclaurin series by termwise integrating the integrand. (The integrals cannot be evaluated by the usual methods of calculus. They define the error function erf z, sine integral Si(z), and Fresnel integrals S(z) and C(z), which occur in statistics, heat conduction, optics, and other applications. These are special so-called higher transcendental functions.)

$$S(z)=∫_0^zsint^2dt$$

Use the following data set. The data represent the heights (in inches) of students in a statistics class.

$$\begin{array}{llllllllll}52 & 54 & 55 & 56 & 56 & 56 & 58 & 59 & 60 & 61 \\ 61 & 63 & 65 & 67 & 68 & 68 & 70 & 71 & 72 & \end{array}$$

Make a box-and-whisker plot of the data.

The file DomesticBeer contains the percentage alcohol, number of calories per 12 ounces, and number of carbohydrates (in grams) per 12 ounces for 152 of the best-selling domestic beers in the United States. Determine whether each of these variables appears to be approximately normally distributed. Support your decision through the use of appropriate statistics and graphs.

Assume that a statistics class consists of 10 females and 30 males, and each day, 12 of the students are randomly selected without replacement. Because the sampling is from a small finite population without replacement, the hypergeometric distribution applies. Using the hypergeometric distribution, find the mean and standard deviation for the number of girls that are selected on the different days.

According to the National Center for Health Statistics, the distribution of heights for 15-year-old males is modeled well by a Normal density curve. For this distribution, a z-score of 0 corresponds to a height of 170 centimeters ( cm}, and a z-score of 1 corresponds to a height of 177.5 cm. The distribution of heights for 16-year-old females is also modeled well by a Normal density curve. For this distribution, a z-score of 0 corresponds to a height of 162.5 cm, and a z-score of 1 corresponds to a height of 169 cm. Paul is 15 years old and 175 cm tall. (a) Find the z-score corresponding to Paul's height. Explain what this value means. (b) Paul's height puts him at the 75th percentile among 15-year-old males. Explain what this means to someone who knows no statistics.

Do medical specialists differ in the amount of time they devote to patient care? To answer this question a statistics practitioner organized a study. The numbers of hours of patient care per week were recorded for five specialists. The experimental design was randomized blocks. The physicians were blocked by age. Can we infer that blocking by age was appropriate?