Through their Roper Reports Worldwide, GfK Roper conducts a global consumer survey to help multinational companies understand different consumer attitudes throughout the world. Within 30 countries, the researchers interview 1000 people aged 13–65. Their samples are designed so that they get 500 males and 500 females in each country. (www.gfkamerica.com) a) Are they using a simple random sample? Explain. b) What kind of design do you think they are using?

GfK Roper Consulting gathers information on consumer preferences around the world to help companies monitor attitudes about health, food, and healthcare products. They asked people in many different cultures how they felt about the following statement: I have a strong preference for regional or traditional products and dishes from where I come from. In a random sample of 800 respondents, 417 of 646 people who live in urban environments agreed (either completely or somewhat) with that statement, compared to 78 out of 154 people who live in rural areas Based on this sample, is there evidence that the percentage of people agreeing with the statement about regional preferences differs between all urban and rural dwellers?

GfK Roper Reports Worldwide surveyed people, requesting them, "How important is acquiring wealth to you?" The percent who responded that it was of more than average importance were: $71.9 \%$ China, $59.6 \%$ France, $76.1 \%$ India, $45.5 \%$ U.K., and $45.3 \%$ U.S. There were about 1500 respondents per country.

c) How would you improve this display?

Find $|\mathbf{u}|, \mathbf{u}+\mathbf{v}, \mathbf{u}-\mathbf{v}, 2 \mathbf{u},$ and $3 \mathbf{u}-2 \mathbf{v}.$ $\mathbf{u}=\langle 5,-2\rangle, \quad \mathbf{v}=\langle- 3,0\rangle$

Using the information provided, including the T1-83/84 calculator screen shot in the margin, determine the probability of each of the two types of error.

Fidelity Magellan is a large cap growth mutual fund and Fidelity Small Cap Stock is a small cap growth mutual fund (Morningstar Funds 500, 2006). The standard deviation for both funds was computed based on a sample of size 26. For Fidelity Magellan, the sample standard deviation is 8.89%; for Fidelity Small Cap Stock, the sample standard deviation is 13.03%. Financial analysts often use the standard deviation as a measure of risk. Conduct a hypothesis test to determine whether the small cap growth fund is riskier than the large cap growth fund. Use $\alpha$= .05 as the level of significance.

For each system, choose the method of solving that seems easier to use. Explain why you made each choice.

$$\left\{\begin{array}{l}{3 x-y=5} \\ {y=4 x+2}\end{array}\right.$$

a. What is the most common way to determine an intelligence test's reliability? b. Why are the Wechsler scales more widely used than the Stanford-Binet test? c. Other than vocabulary and problem solving methods, what else might cause intelligence tests to be culturally biased?

A cylindrical rod of diameter 6.7 mm fabricated from a 70Cu-30Zn brass alloy is subjected to rotating–bending load cycling; test results (as S–N behavior). If the maximum and minimum loads are +120 N and –120 N, respectively, determine its fatigue life. Assume that the separation between load bearing points is 67.5 mm.

The area of a rectangle is 400

$$in^2$$

. If the length of the rectangle is 40 in., what is the width?

Simplify the Distance Formula for θ1 - θ2 = 90°, Is the simplification what you expected? Explain.

A triangular region has a base that connects the vertices (0, 0) and (b, 0), and a third vertex at (a, h), where $a\gt 0$, $b \gt 0$, and $h\gt 0$.

Show that the centroid of the triangle is $\left( \frac { a + b } { 3 } , \frac { h } { 3 } \right)$.

Determine whether the given set is a subspace of $R^4$. Justify your answer,

$$\begin{Bmatrix}\begin{bmatrix}u_1\\u_2\\u_3\\u_4\end{bmatrix}\text{in }R^4: u_2=5u_3,u_1=0,\text{ and } u_4=0\end{Bmatrix}$$

In what type of units is the volume of a solid measured?