Nationally the proportion of red cars on the road is 0.12. A statistically minded fan of the Philadelphia Phillies (whose team color is red) wonders if Phillies fans are more likely to drive red cars, One day during a home game, he takes a random sample of 210 cars parked at Citizens Bank Park (the Phillies home field) and counts 35 red cars. Explain why there is some evidence for the alternative hypothesis.

Nationally, the proportion of red cars on the road is 0.12. A statistically minded fan of the Philadelphia Phillies (whose team color is red) wonders if Phillies fans are more likely to drive red cars. One day during a home game, he selects a random sample of 210 cars parked at Citizens Bank Park (the Phillies home field), and counts 35 red cars.

What conclusion would you make?

A survey of 25 randomly selected customers found the following ages (in years):

$$\begin{array}{lllll}20 & 32 & 34 & 29 & 30 \\ 30 & 30 & 14 & 29 & 11 \\ 38 & 22 & 44 & 48 & 26 \\ 25 & 22 & 32 & 35 & 32 \\ 35 & 42 & 44 & 44 & 48\end{array}$$

The mean was $31.84$ years and the standard deviation was $9.84$ years.

b) Is the alternative one- or two-sided?

The number of alternative fuel vehicles running on E85, fuel that is up to $85\%$ plant-derived ethanol , increased exponentially in the US between 2003 and 2008 . Use this information to complete the missing table values.

$$\begin{array}{c|c|c|c|c|c} \hline \text{Year} & 2004 & 2005 & 2006 & 2007 & 2008\\ \hline \text{Number of E85 vehicles} & 211,800 & ? & ? & ? & 450,327\\ \hline \end{array}$$

Nationally, the proportion of red cars on the road is 0.12. A statistically minded fan of the Philadelphia Phillies (whose team color is red) wonders if Phillies fans are more likely to drive red cars. One day during a home game, he takes a random sample of 210 cars parked at Citizens Bank Park (the Phillies home field), and counts 35 red cars. State appropriate hypotheses for performing a significance test. Be sure to define the parameter of interest.

Consider A-E, five mutually exclusive alternatives. The interest rate is 8%. If all the alternatives have a 12-year useful life and no salvage value, which alternative should be selected?

$$\begin{array}{llllll}\text { For first } 6 \text { years } & 125 & 150 & 100 & 125 & 150\end{array}$$

$$\begin{array}{llllll}\text { For last 6 years } & 40 & 80 & 120 & 50 & 50\end{array}$$

Select the best answer. After once again losing a football game to the archrival, a college's alumni association conducted a survey to see if alumni were in favor of firing the coach. An SRS of 100 alumni from the population of all living alumni was taken, and 64 of the alumni in the sample were in favor of firing the coach. Suppose you wish to see if a majority of living alumni are in favor of firing the coach. The appropriate test statistic is (a)

$$z = \frac { 0.64 - 0.5 } { \sqrt { \frac { 0.64 ( 0.36 ) } { 100 } } }$$

(b)

$$t = \frac { 0.64 - 0.5 } { \sqrt { \frac { 0.64 ( 0.36 ) } { 100 } } }$$

(c)

$$z = \frac { 0.64 - 0.5 } { \sqrt { \frac { 0.5 ( 0.5 ) } { 100 } } }$$

(d)

$$z = \frac { 0.64 - 0.5 } { \sqrt { \frac { 0.64 ( 0.36 ) } { 64 } } }$$

(e)

$$z = \frac { 0.5 - 0.64 } { \sqrt { \frac { 0.5 ( 0.5 ) } { 100 } } }$$

An alternative method for preparing pure iron from Fe$_2$O$_3$ is by reaction with carbon monoxide:

Fe$_2$O$_3$ + CO $\rarr$ Fe + CO$_2$ (Unbalanced)

(a) Balance the equation.

(b) How many grams of CO are needed to react with 3.02 g of Fe$_2$O$_3$?

(c ) How many grams of CO are needed to react with 1.68 mol of Fe$_2$O$_3$?

Alternative definitions of means Consider the function

$$f(t)=\frac{\int_{a}^{b} x^{t+1} d x}{\int_{a}^{b} x^{t} d x}$$

Show that the following means can be defined in terms off.

Arithmetic mean: $f(0)=\frac{a+b}{2}$

An alternative to the logistic model for restricted population growth is the Beverton-Holt recruitment curve. Here the recursion model is $N_{t+1}=\frac{c N_{t}}{1+(c-1) N_{t} / K}$ where K is the carrying capacity and c is the per capita growth factor. If K = 50 and c = 1.7, plot some points on the graph of $N_t$ for the following values of the initial population: $N_{0}=10,30,70.$

In a drawer are two coins. They look the same, but one coin produces heads 90% of the time when spun while the other one produces heads only 30% of the time. You select one of the coins. You are allowed to spin it once and then must decide whether the coin is the 90%-or the 30%-head coin. Your null hypothesis is that your coin produces 90% heads. What is the alternative hypothesis?

A firm is considering two alternatives that have no salvage value. At the end of 5 years, another B may be purchased with the same cost, benefits, and so forth.

(a) Graph the EUAC or EUA W for the alternatives. Construct a choice table for interest rates from 0% to 100%

(b) If the MARR is 15%, which alternative should be selected?

Compare the alternatives below on the basis of their capitalized costs with adjustments made for inflation. Use i =12% per year and f = 3% per year.

$$\begin{array}{lcc} \text { Alternative } & \mathrm{X} & \mathrm{Y} \\ \hline \text { First cost, } \$ & -18,500,000 & -9,000,000 \\ \text { AOC, } \$ \text { per year } & -25,000 & -10,000 \\ \text { Salvage value, } \$ & 105,000 & 82,000 \\ \text { Life, years } & \infty & 10 \\ \hline \end{array}$$

Use the information form previous exercise.

a. Which class had the highest sample mean, and which class had the lowest sample mean? (1 is for freshman, 2 is for sophomore, and so on.)

b. Write out the null and alternative hypotheses for the effect of class on schoolwork.

c. Identify the F-value from the output.

d. Assuming that you found an association between class and schoolwork would that show that class caused the different levels of schoolwork? Explain.