If (0.57, 0.63) is a 50% confidence interval for p, what does $\frac{k}{n}$ equal, and how many observations were taken?

An international textile company’s North America Division must decide which type of fabric cutting machines it will use—straight knife or round knife. The estimates are summarized below. Compare them on the basis of annual worths values at i = 10% per year using (a) factors, and (b) single-cell spreadsheet functions.

$$\begin{array}{lcc} & \text { Round Knife } & \text { Straight Knife } \\ \hline \hline \text { First cost, } \$ & -250,000 & -170,000 \\ \text { AOC, \$/year } & -31,000 & -35,000 \\ \text { Overhaul in year } 2, \$ & - & -26,000 \\ \text { Salvage value, } \$ & 40,000 & 10,000 \\ \text { Life, years } & 6 & 4 \\ \hline \end{array}$$

Find the value of k so that each remainder. is zero. $\frac{x^{3}-k x^{2}+2 x-4}{x-2}$

a. Write the equation of the ellipse in standard form. b. Identify the center, vertices, endpoints of the minor axis, and foci.

$$36 x^{2}+100 y^{2}-180 x+800 y+925=0$$

A physician who has a group of thirty-eight female patients aged 18 to 24 on a special diet wishes to estimate the effect of the diet on total serum cholesterol. For this group, their average serum cholesterol is 188.4 (measured in mg/100mL). Because of a large-scale government study, the physician is willing to assume that the total serum cholesterol measurements are normally distributed with standard deviation of $\sigma$ = 40.7. Find a 95% confidence interval of the mean serum cholesterol of patients on the special diet. Does the diet seem to have any effect on their serum cholesterol, given that the national average for women aged 18 to 24 is 192.0?

Graph each quadratic function. Give the largest open interval of the domain over which the function is increasing. $f(x)=2 x^{2}-4 x+5$

The relationship between school funding and student performance continues to be a hotly debated political and philosophical issue. Typical of the data available are the following figures, showing the per-pupil expenditures and graduation rate for twenty-six randomly chosen districts in Massachusetts. Graph the data and superimpose the least squares line, y = a + bx. What would you conclude about the xy-relationship? Use the following sums:

$$\begin{aligned} &\sum_{i=1}^{26} x_{i}=360 \quad \sum_{i=1}^{26} y_{i}=2,256.6\\ &\sum_{i=1}^{26} x_{i}^{2}=5,365.08 \quad \sum_{i=1}^{26} x_{i} y_{i}=31,402 \end{aligned}$$

$$\begin{array}{lcc} \hline & \text { Spending } \\ & \text { per Pupil } \\ \text { District } & \text { (in }1000 \mathrm{s}), x & \text { Graduation Rate, } y \\ \hline \end{array}$$

$$\begin{array}{lcc} \text { Dighton-Rehoboth } & \$ 10.0 & 88.7 \\ \text { Duxbury } & \$ 10.2 & 93.2 \\ \text { Tyngsborough } & \$ 10.2 & 95.1 \\ \text { Lynnfield } & \$ 10.3 & 94.0 \\ \text { Southwick-Tolland } & \$ 10.3 & 88.3 \\ \text { Clinton } & \$ 10.8 & 89.9 \\ \text { Athol-Royalston } & \$ 11.0 & 67.7 \\ \text { Tantasqua } & \$ 11.0 & 90.2 \\ \text { Ayer } & \$ 11.2 & 95.5 \\ \text { Adams-Cheshire } & \$ 11.6 & 75.2 \\ \text { Danvers } & \$ 12.1 & 84.6 \\ \text { Lee } & \$ 12.3 & 85.0 \\ \text { Needham } & \$ 12.6 & 94.8 \\ \text { New Bedford } & \$ 12.7 & 56.1 \\ \text { Springfield } & \$ 12.9 & 54.4 \\ \text { Manchester Essex } & \$ 13.0 & 97.9 \\ \text { Dedham } & \$ 13.9 & 83.0 \\ \text { Lexington } & \$ 14.5 & 94.0 \\ \text { Chatham } & \$ 14.7 & 91.4 \\ \text { Newton } & \$ 15.5 & 94.2 \\ \text { Blackstone Valley } & \$ 16.4 & 97.2 \\ \text { Concord Carlisle } & \$ 17.5 & 94.4 \\ \text { Pathfinder } & \$ 18.1 & 78.6 \\ \text { Nantucket } & \$ 20.8 & 87.6 \\ \text { Essex } & \$ 22.4 & 93.3 \\ \text { Provincetown } & \$ 24.0 & 92.3 \end{array}$$

Suppose a coin is to be tossed n times for the purpose of estimating p, where p = P(heads). How large must n be to guarantee that the length of the 99% confidence interval for p will be less than 0.02?

Suppose a sample of size n is to be drawn from a normal distribution where $\sigma$ is known to be 14.3. How large does n have to be to guarantee that the length of the 95% confidence interval for $\mu$ will be less than 3.06?

Let $X_{1}, X_{2}, \ldots, X_{n}$ be a random sample of size n from the Poisson distribution,

$$p_{X}(k ; \lambda)=\frac{e^{-\lambda} \lambda^{k}}{k !}, k= 0,1, \ldots$$

Show that $\hat{\lambda}=\frac{1}{n} \sum_{i=1}^{n} X_{i}$ is an efficient estimator for $\lambda$.

For each of the polynomial functions given, identify the leading term of the function and describe the end behavior of the function based on your analysis of the leading term. a. $h(x)=2 x(x+5)(x-1)^{2}$ b. $k(-x)=-(x+3)(x-4)^2$ c. $g(x)=x^{6}-7 x^{5}+13 x^{4}+7 x^{3}-34 x^{2}+4 x+24$ d. $f(x)=x^{3}-4 x^{2}+x+6$

The Wind Chill Factor (WCF) measures how cold it feels with a given air temperature (T, in degrees Fahrenheit) and wind speed (V, in miles per hour). One formula for the WCF follows: $\mathrm{WCF}=35.7+0.6 T-35.7\left(v^{0.16}\right)+0.43 T\left(v^{0.16}\right)$ Create a table showing WCFs for temperatures ranging from -20 to 55 in steps of 5, and wind speeds ranging from 0 to 55 in steps of 5. Write this to a file wcftable.dat. If you have version R2016a or later, write the script as a live script.

Suppose n = 36 observations are taken from a normal distribution where $\sigma=8.0$ for the purpose of testing $H_{0}: \mu=60$ versus $H_{1}: \mu \neq 60$ at the $\alpha=0.07$ level of significance. The lead investigator skipped statistics class the day decision rules were being discussed and intends to reject $H_{0}$ if $\bar{y}$ falls in the region $\left(60-\bar{y}^{*}, 60+\bar{y}^{*}\right)$. (a) Find $\bar{y}^{*}$ (b) What is the power of the test when $\mu=62 ?$ (c) What would the power of the test be when $\mu=62$ if the critical region had been defined the correct way?

For each separate case below, follow the three-step process for adjusting the accrued revenue account at December 31. Step 1: Determine what the current account balance equals. Step 2: Determine what the current account balance should equal. Step 3: Record the December 31 adjusting entry to get from step 1 to step 2. Assume no other adjusting entries are made during the year. a. Accounts Receivable. At year-end, the Krug Company has completed services of $19,000 for a client, but the client has not yet been billed for those services. b. Interest Receivable. At year-end, the company has earned, but not yet recorded,$390 of interest earned from its investments in government bonds. c. Accounts Receivable. A painting company collects fees when jobs are complete. The work for one customer, whose job was bid at $1,300, has been completed, but the customer has not yet been billed.