In a study designed to investigate the effects of a strong magnetic field on the early development of mice, ten cages, each containing three 30-day-old albino female mice, were subjected for a period of 12 days to a magnetic field having an average strength of 80 Oe/cm. Thirty other mice, housed in ten similar cages, were not put in the magnetic field and served as controls. Listed in the table are the weight gains, in grams, for each of the twenty sets of mice.

$$\scriptstyle \begin{array}{c} \hline \text { In Magnetic Field } & \text { Not in Magnetic Field } \\ \hline\end{array}$$

$$\scriptstyle\begin{array}{cccc} \text { Cage } & \text { Weight Gain (g) } & \text { Cage } & \text { Weight Gain (g) } \\ \hline 1 & 22.8 & 11 & 23.5 \\ 2 & 10.2 & 12 & 31.0 \\ 3 & 20.8 & 13 & 19.5 \\ 4 & 27.0 & 14 & 26.2 \\ 5 & 19.2 & 15 & 26.5 \\ 6 & 9.0 & 16 & 25.2 \\ 7 & 14.2 & 17 & 24.5 \\ 8 & 19.8 & 18 & 23.8 \\ 9 & 14.5 & 19 & 27.8 \\ 10 & 14.8 & 20 & 22.0 \\ \hline \end{array}$$

Test whether the variances of the two sets of weight gains are significantly different. Let $\alpha=0.05 .$ For the mice in the magnetic field, $s_{X}=5.67 ;$ for the other mice, $s_{Y}=3.18$.

Monochromatic light at 577 nm illuminates a diffraction grating with 325 lines/mm. Determine the highest order that can be observed with this grating at the given wavelength.

Poverty Point is the name given to a number of widely scattered archaeological sites throughout Louisiana, Mississippi, and Arkansas. These are the remains of a society thought to have flourished during the period from 1700 to 500 B.C. Among their characteristic artifacts are ornaments that were fashioned out of clay and then baked. The following table shows the dates (in years B.C.) associated with four of these baked clay ornaments found in two different Poverty Point sites, Terral Lewis and Jaketown (94). The averages for the two samples are 1133.0 and 1013.5, respectively. Is it believable that these two settlements developed the technology to manufacture baked clay ornaments at the same time? Set up and test an appropriate $H_{0}$ against a two-sided $H_{1}$ at the $\alpha=0.05$ level of significance. For these data $s_{x}=266.9$ and $s_{y}=224.3$.

$$\begin{array}{cc}\hline \text { Terral Lewis Estimates, } x_{i} & \text { Jaketown Estimates, } y_{i} \\ \hline 1492 & 1346 \\ 1169 & 942 \\ 883 & 908 \\ 988 & 858 \\ \hline\end{array}$$

Factor out the least power of the variable or variable expression. Assume all variables represent positive real numbers. $7(5 t+3)^{-5 / 3}+14(5 t+3)^{-2 / 3}-21(5 t+3)^{1 / 3}$

Work each problem. Let U={1, 2, 3, 4, 5} and A={1, 2, 3}. Find A'.

A major source of "mercury poisoning" comes from the ingestion of methylmercury $\left(\mathrm{CH}_{3} \mathrm{Hg}^{+}\right),$ which is found in contaminated fish. Among the questions pursued by medical investigators trying to understand the nature of this particular health problem is whether methylmercury is equally hazardous to men and women. The following are the half-lives of methylmercury in the systems of six women and nine men who volunteered for a study where each subject was given an oral administration of $\mathrm{CH}_{3} \mathrm{Hg}^{+}$. Is there evidence here that women metabolize methylmercury at a different rate than men do? Do an appropriate two sample t test at the $\alpha=0.01$ level of significance. The two sample standard deviations for these data are $s_{X}=15.1$ and $s_{Y}=8.1$

$$\begin{array}{c} \hline \text { Methylmercury }\left(\mathrm{CH}_{3} \mathrm{Hg}^{+}\right) & \text {Half-Lives (in days) } \\ \text { Females, } x_{i} & \text { Males, } y_{i} \\ \hline 52 & 72 \\ 69 & 88 \\ 73 & 87 \\ 88 & 74 \\ 87 & 78 \\ 56 & 70 \\ & 78 \\ & 93 \\ & 74 \\ \hline \end{array}$$

As the United States has struggled with the growing obesity of its citizens, diets have become big business. Among the many competing regimens for those seeking weight reduction are the Atkins and Zone diets. In a comparison of these two diets for one-year weight loss, a study found that seventy-seven subjects on the Atkins diet had an average weight loss of $\bar{x}=-4.7 \mathrm{kg}$ and a sample standard deviation of $s_{X}=7.05 \mathrm{kg}.$ Similar figures for the seventy-nine people on the Zone diet were $\bar{y}=-1.6 \mathrm{kg}$ and $s_{Y}=5.36 \mathrm{kg}.$ Is the greater reduction with the Atkins diet statistically significant? Test for $\alpha=0.05$.

For the approximate two-sample t test described, it will be true that

$$v<n+m-2$$

Why is that a disadvantage for the approximate test? That is, why is it better to use the Theorem 9.2.1 version of the t test if, in fact, $\sigma_{X}^{2}=\sigma_{Y}^{2}$?

Find $f^{\prime}(x)$. $f(x)=3 x^{e}-2 e^{x}$

Refer to the n=5 data points $\left(x_{1}, y_{1}\right)=(0,4)$ $\left(x_{2}, y_{2}\right)=(1,5),\left(x_{3}, y_{3}\right)=(2,7),\left(x_{4}, y_{4}\right)=(3,9)$, and $\left(x_{5}, y_{5}\right)=(4,13)$. Calculate the indicated sum or product of sums. $\sum_{k=1}^{5} x_{k} y_{k}$

Seven different financing plans with their D-E mixes and costs of debt and equity capital for a new innovations project are summarized below. Use the data to determine what mix of debt and equity capital will result in the lowest WACC. $$ \begin{array} \text{ } & \text{Debt Capital} & \text{ } & \text{Equity Capital} & \text{ }\\ \hline \text{Plan} & \text{Percentage} & \text{Rate, \\%} & \text{Percentage} & \text{Rate, \\%}\\ \hline \text{1} & \text{100} & \text{14.5} & \text{-} & \text{-}\\ \text{2} & \text{70} & \text{13.0} & \text{30} & \text{7.8}\\ \text{3} & \text{65} & \text{12.0} & \text{35} & \text{7.8}\\ \text{4} & \text{50} & \text{11.5} & \text{50} & \text{7.9}\\ \text{5} & \text{35} & \text{9.9} & \text{65} & \text{9.8}\\ \text{6} & \text{20} & \text{12.4} & \text{80} & \text{12.5}\\ \text{7} & \text{-} & \text{-} & \text{100} & \text{12.5}\\ \hline \end{array} $$

A large crate of mass m is placed on the back of a truck but not tied down. As the truck accelerates forward with an acceleration a, the crate remains at rest relative to the truck. What force causes the crate to accelerate forward? the force of gravity.

You are given the 2012 value of a product and the rate at which the value is expected to change during the next 5 years. Use this information to write a linear equation that gives the dollar value V of the product in terms of the year. (Let t=12 represent 2012.)

$$\begin{matrix} \text{2012 Value} & \text{Rate}\\ \text{\$245,000} & \text{\$5600 increase per year}\\ \end{matrix}$$

Out of one hundred twenty senior citizens polled, sixty-five favored a complete overhaul of the health care system while fifty-five preferred more modest changes. When the same choice was put to eighty-five first-time voters, forty said they were in favor of major reform while forty-five opted for minor revisions.