Although the chi-square homogeneity test and the chi-square independence test use essentially the same basic procedure, the context of the two tests are quite different. Explain the difference.

Madison Finance opened two branches on September $1\space (t = 0)$. Branch $A$ is located in an established industrial park, and branch $B$ is located in a fast-growing new development. The net rates at which money was deposited into branch $A$ and branch $B$ in the first $180$ business days are given by the graphs of $f$ and $g$, respectively. Which branch has a larger amount on deposit at the end of $180$ business days? Justify your answer.

Determine whether the following series converge or diverge using the properties and tests introduced in the sections. $\sum_{k=1}^{\infty} \frac{3^{k}}{k^{2}+1}$

Based on experience, the Ball Corporation’s aluminum can manufacturing facility in Ft. Atkinson, Wisconsin, knows that the metal thickness of incoming shipments has a mean of 0.2731 mm with a standard deviation of 0.000959 mm.

(a) A certain shipment has a diameter of 0.2761. Find the standardized z-score for this shipment.

(b) Is this an outlier?

Nuclear scientists have synthes ized approximately 1600 nuclein ot known in nature. More might be discovered with heavy-ion bombardment using high-energy particle accelerators. Complete and balance the following reactions, which involve heavy-ion bombardments:

$$_ { 20 } ^ { 40 } \mathrm { Ca } + ^ { 248 } _{96} \mathrm { Cm } \longrightarrow _ { 62 } ^ { 147 } \mathrm { Sm } + \ ?$$

On the first day of its fiscal year, Ebert Company issued $50,000,000 of 10-year, 7% bonds to finance its operations. Interest is payable semiannually. The bonds were issued at a market (effective) interest rate of 9%, resulting in Ebert Company receiving cash of$43,495,895. The company uses the interest method.

c. Explain why the company was able to issue the bonds for only $43,495,895 rather than for the face amount of$50,000,000.

Use the algebraic tests to check for symmetry with respect to both axes and the origin. (Select all that apply.)

x-y^2=15

-x-axis symmetry -y-axis symmetry -origin symmetry -no symmetry

Research credit and the cost of credit from a variety of institutions, such as those listed below. Convert the rates to decimals, and use a number line to rank them in order from the lowest interest rate to the highest.

• consumer finance company
• revolving charge account
• travel and entertainment credit card
• credit union
• commercial bank

Positive decimals closer to zero on a number line are less than decimals closer to $1$ .

Determine whether the following series converge or diverge using the properties and tests introduced in the sections. $\sum_{k=3}^{\infty} \frac{4}{k \sqrt{\ln k}}$

The United States Department of Agriculture (USDA) reports that, under its standard inspection system, one in every 100 slaughtered chickens passes inspection for fecal contamination. The probability of part a was based on a USDA study which found that 306 of 32,075 chicken carcasses passed inspection for fecal contamination. Do you agree with the USDA’s statement about the likelihood of a slaughtered chicken passing inspection for fecal contamination?

Read each brief report of statistical research, and identify a) whether it was an observational study or an experiment. If it was an observational study, identify (if possible) b) whether it was retrospective or prospective. c) the subjects studied and how they were selected. d) the parameter of interest. e) the nature and scope of the conclusion the study can reach. If it was an experiment, identify (if possible) b) the subjects studied. c) the factor(s) in the experiment and the number of levels for each. d) the number of treatments. e) the response variable measured. f) the design (completely randomized, blocked, or matched). g) whether it was blind (or double-blind). h) the nature and scope of the conclusion the experiment can reach. Over a 4-month period, among 30 people with bipolar disorder, patients who were given a high dose (10 g/day) of omega-3 fats from fish oil improved more than those given a placebo.

Explain whether or not each of the following would ever differ for two random samples of the same size from the same population. The sample mean

$$\overline{x}$$

The standard deviation of the sampling distribution of

$$\overline{x}$$

The standard error of

$$\overline{x}$$

The standardized z-score for the observed value of

$$\overline{x}$$

The population mean µ

Determine whether there is a relative maximum, a relative minimum, a saddle point, or insufficient information to determine the nature of the function f(x, y) at the critical point $\left(x_{0}, y_{0}\right)$. $f_{x x}\left(x_{0}, y_{0}\right)=8, f_{y y}\left(x_{0}, y_{0}\right)=7, f_{x y}\left(x_{0}, y_{0}\right)=9$

Use any of the comparison tests to determine whether each series converges or diverges. $\sum_{k=1}^{\infty} \frac{1+3 \sqrt{k}}{k^{2}}$