Study the entries and answer the questions that follow. The prefixes ambi and amphi mean "both" or "around." The roots luc and lum mean "light." The prefix super means "above" or "over." The root magn means "great." You might use a lamp to _____ your desktop so that you can see your work. If the filament in the light bulb does not become _____, you will know that the bulb is burned out.

The number of years employed was determined for a sample of employees at a large company. The following output presents a confidence interval for the population mean length of employment.

$$\begin{array}{l} \hline \text{The assumed sigma = 8.0000}\\ \\ \begin{array}{lrrrrl} \text{Variable} & \text{N} & \text{Mean} & \text{SE Mean} & 98\% & \text{CI}\\ \text{X} & 58 & 2.657 & 1.0505 & (0.1233, & 5.1007)\\ \end{array}\\ \hline \end{array}$$

a. Fill in the blanks. We are $\_\_\_\_\_\_\_\_\_\_\_\_\_$ confident that the population mean number of years employed is between $\_\_\_\_\_\_\_\_\_\_\_\_\_$ and $\_\_\_\_\_\_\_\_\_\_\_\_\_$.

b. Use the appropriate critical value along with the information in the computer output to construct a $95\%$ confidence interval.

c. Find the sample size needed so that the $98\%$ confidence interval will have a margin of error of $1.0$.

d. Find the sample size needed so that the $95\%$ confidence interval will have a margin of error of $1.0$.

A random sample of n=64 observations has a mean $\mu$=29.1 and a standard deviation s=3.9. a. Give a point estimate of the population mean $\mu$ and find the margin of error for your estimate. b. Find a 90% confidence interval for $\mu$. What does "90% confident" mean? c. Find a 90% lower confidence bound for the population mean $\mu$. Why is this bound different from the lower confidence limit in part b? d. How many observations do you need to estimate $\mu$ to within .5, with probability equal to .95.

If a monic polynomial with integer coefficients has a root in $\mathbb{Q}$, show that this root must be an integer.

Write the equation of the square root or cube root function whose graph is shown in the exercise.

f(x)=

Suppose a simple random sample of size 50 is selected from a population with $\sigma= 10$. Find the value of the standard error of the mean in each of the following cases (use the finite population correction factor if appropriate).

The population size is $N = 500.$

A helical compression spring is made with oil-tempered wire with wire diameter of 0.2 in, mean coil diameter of 2 in, a total of 12 coils, a free length of 5 in, with squared ends. a) Find the solid length. b) Find the force necessary to deflect the spring to its solid length. c) Find the factor of safety guarding against yielding when the spring is compressed to its solid length.

The formula $v=\sqrt{2 g h}$ gives the velocity $v$, in feet per second, of an object when it falls $h$ feet accelerated by gravity $g$, in feet per second squared. If $g$ is approximately 32 feet per second squared, discover how far an object has fallen if its velocity is 80 feet per second.

The following ANOVA summary table is for a multiple regression model with two independent variables:

$$\begin{array}{lcccc} Source & \text{Degrees of Freedom} & \text{Sum of Squares} & \text{Mean Squares} & \boldsymbol{F} \\ \hline Regression & 2 & 30 & & \\ Error & 10 & 120 & & \\ \hline Total & 12 & 150 & \end{array}$$

a. Determine the regression mean square (MSR) and the mean square error (MSE).

b. Compute the overall $F_{S T A T}$ test statistic.

c. Determine whether there is a significant relationship between Y and the two independent variables at the 0.05 level of significance.

d. Compute the coefficient of multiple determination, $r^2$, and interpret its meaning.

e. Compute the adjusted $r^2$.

Complete the sentences by inferring information about the italicized word from its context. Few people talked to Billy, the $\mathit{pariah}$ of the town, because he...

A study of genetic factors related to coronary heart disease (CHD) was performed as a substudy within the ARIC Study. The data in the table below were provided by ethnic group for high-density lipoprotein $(\mathrm{HDL})$ cholesterol $(\mathrm{mg} / \mathrm{dL})$.

Mean HDL cholesterol (mg/dL) by ethnic group

What is the standard error of the mean for each group?

In the third week of July, a random sample of 40 farming regions gave a sample mean of $\bar{x}=\$ 6.88$ per 100 pounds of watermelon. Assume that $\sigma$ is known to be $1.92 per 100 pounds. Find a 90% confidence interval for the population mean price (per 100 pounds) that farmers in this region get for their watermelon crop. What is the margin of error?

Estimate each square root or cube root to the nearest integer. $\sqrt[3]{415}$

The fast-food franchiser in Exercise 11.51 was unable to provide enough evidence that the site is acceptable. She is concerned that she may be missing an opportunity to locate the restaurant in a profitable location. She feels that if the actual mean is 104, the restaurant is likely to be very successful. Determine the probability of a Type II error when the mean is 104. Suggest ways to improve this probability.