A mutual fund is a professionally managed investment that can be sold to the general public. Mutual funds can be specialized into different categories such as healthcare-related or technology-related mutual funds. The following table lists the 3-month rates of return, in percent, for samples of health-care related and technology-related mutual funds, as reported by Morningstar, an independent investment research company. \

$$\begin{array}{ccccc|ccccc} \hline & {\text { Healthcare }} & {\text { }} &{\text { }} &{\text { }} &{\text { Technology }} \\ \hline 9.7 & 9.5 & 7.6 & 6.8 & 6.7 & 6.5 & 6.4 & 6.4 & 6.2 & 4.9 \\ 6.7 & 6.6 & 4.6 & 3.9 & 3.9 & 4.6 & 4.6 & 4.2 & 3.6 & 3.2 \\ 3.7 & 3.3 & 3.0 & 0.8 & -9.9 & 2.9 & 2.8 & 2.7 & 2.5 & \\ \hline \end{array}$$

Use the technology of your choice to answer the following questions. Explain your answers. a. If you had to choose between the use of pooled t-procedures and nonpooled t -procedures here, which would you choose? b. Is it reasonable to use the type of procedure that you selected in part (a)?

Refer to the Minitab print out regarding prehistoric pottery. Mini tab calls the explanatory variable the predictor variable. Which is the predictor variable, the diameter of the pot or the height?

For each function of three variables, find the partials a. $f_{x},$ b. $f_{y},$ and c. $f_{z}$. $f=e^{x^{2}+y^{2}+z^{2}}$

Answer true or false and explain your answer: For a fixed sample size, decreasing the significance level of a hypothesis test results in an increase in the probability of making a Type II error.

The service department of a large automobile dealership records the odometer readings of cars that it repairs and determines that the distribution of miles driven per year by all of its customers has a mean of 14,000 miles and a standard deviation of 4000 miles. The distribution is skewed to the right. Suppose a random sample of 12 cars is taken from the dealership's service records, and the mean number of miles per year driven by these cars, $\bar{x},$ is calculated. What is the mean of the sampling distribution of $\bar{x} ?$

Female mosquitoes (Culex pipiens) feed on blood (only the females drink blood) and then lay several hundred eggs. In this way each mosquito can, on the average, breed another 300 mosquitoes in about 9 days. Find the number of great-grandchildren mosquitoes that will be descended from one female mosquito, assuming that all eggs hatch and mature.

Use the following steps (i) through (v) for all hypothesis tests. (i) What is the level of significance? State the null and alternate hypotheses. (ii) What sampling distribution will you use? What assumptions are you making? What is the value of the sample test statistic? (iii) Find (or estimate) the P-value. Sketch the sampling distribution and show the area corresponding to the P-value. (iv) Based on your answers in parts (i) to (iii), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level $\alpha$? (v) Interpret your conclusion in the context of the application. Carboxyhemoglobin is formed when hemoglobin is exposed to carbon monoxide. Heavy smokers tend to have a high percentage of carboxyhemoglobin in their blood. Let x be a random variable representing percentage of carboxyhemoglobin in the blood. For a person who is a regular heavy smoker, x has a distribution that is approximately normal. A random sample of n = 12 blood tests given to a heavy smoker gave the following results (percent carboxyhemoglobin in the blood).

$$\begin{array}{rrrrrr} 9.1 & 9.5 & 10.2 & 9.8 & 11.3 & 12.2 \\ 11.6 & 10.3 & 8.9 & 9.7 & 13.4 & 9.9 \end{array}$$

Use the given data to find a 99% confidence interval for $\mu$ for this patient.

Find $\frac{d}{d x}\left(\frac{x-2}{x+2}\right)^{3}$ and simplify your answer.

Find each integral by whatever means are necessary (either substitution or tables). $\int \frac{x}{\sqrt{1-x^{2}}} d x$

The school newspaper is planning an article on family-friendly places to stay over spring break at a nearby beach town. The editors intend to call 4 randomly chosen hotels to ask about their amenities for families with children. They have an alphabetized list of all 28 hotels in the town. Describe how to select an SRS of 4 hotels using a random number generator.

The lifetime of a bearing (in years) follows the Weibull distribution with parameters $\alpha=1.5$ and $\beta=0.8.$ a. What is the probability that a bearing lasts more than 1 year? b. What is the probability that a bearing lasts less than 2 years?

Suppose x has a mound-shaped distribution with $\sigma=9$. A random sample of size 36 has sample mean 20. Explain the meaning of the confidence interval you computed.

Identify an important reason for grouping data.

Graph each function showing all relative extreme points and inflection points. $f(x)=x^{4}+4 x^{3}+17$