An opinion poll based on a small sample can be unrepresentative of the population. To see why, assume that 40% of the electorate favors a certain candidate. If a random sample of 7 is asked their preference, what is the probability that a majority will favor this candidate?

The mean breaking strength of a certain type of fiber is required to be at least 200 psi. Past experience indicates that the standard deviation of breaking strength is 5 psi. If a sample of 8 pieces of fiber yielded breakage at the following pressures,

$$\begin{matrix} \text{210} & \text{198}\\ \text{195} & \text{202}\\ \text{197.4} & \text{196}\\ \text{199} & \text{195.5}\\ \end{matrix}$$

would you conclude, at the 5 percent level of significance, that the fiber is unacceptable? What about at the 10 percent level of significance?

An opinion poll asks a sample of 500 adults whether they favor giving parents of school-age children vouchers that can be exchanged for education at any public or private school of their choice. Each school would be paid by the government on the basis of how many vouchers it collected. Suppose that in fact 45% of the population favor this idea. What is the probability that more than half of the sample are in favor? (Assume that the sample is an SRS.)

To test $H_{0}: \mu=80$ versus $H_{1}: \mu<80$, a simple random sample of size n=22 is obtained from a population that is known to be normally distributed.

If $\bar{x}=76.9$ and s=8.5, compute the test statistic.

Let $\mathbf{u}=(3,2,-1), \mathbf{v}=(0,2,-3)$, and $\mathbf{w}=(2,6,7)$. Compute the indicated vectors. (a) $(\mathbf{u} \times \mathbf{v}) \times(\mathbf{v} \times \mathbf{w})$ (b) $\mathbf{u} \times(\mathbf{v}-2 \mathbf{w})$ (c) $(\mathbf{u} \times \mathbf{v})-2 \mathbf{w}$.

A software company is trying to decide whether to produce an upgrade of one of its programs. Customers would have to pay $100 for the upgrade. For the upgrade to be profitable, the company has to sell it to more than 20% of their customers. You contact a random sample of 60 customers and find that 16 would be willing to pay$100 for the upgrade. Do the sample data give convincing evidence at the $\alpha=0.05$ significance level that more than 20% of the company's customers are willing to purchase the upgrade?

What is the law of conservation of mass?

Draw an area model to multiply $1.1 \times 2.4$.

Two horizontal forces act on a 2.5 kg chopping block that can slide over a frictionless kitchen counter, which lies in an xy plane. One force is

$$\vec { F } _ { 1 } = ( 3.0 \mathrm { N } ) \hat { \mathrm { i } } + ( 4.0 \mathrm { N } ) \hat { \mathrm { j } }$$

. Find the acceleration of the chopping block in unit-vector notation when the other force is (a)

$$\vec { F } _ { 2 } = ( - 3.0 \mathrm { N } ) \hat { \mathrm { i } } + ( - 4.0 \mathrm { N } ) \hat { \mathrm { j } }$$

, (b)

$$\vec { F } _ { 2 } = ( - 3.0 \mathrm { N } ) \hat { \mathrm { i } } + ( 4.0 \mathrm { N } ) \hat { \mathrm { j } }$$

, and (c)

$$\vec { F } _ { 2 } = ( 3.0 \mathrm { N } ) \hat { \mathrm { i } } + ( - 4.0 \mathrm { N } ) \hat { \mathrm { j } }$$

.

The following topics related to irrational numbers are appropriate for either individual or group research projects. A report should be given to the class on the researched topic. The Golden Rectangle in Art and Architecture

A software company is trying to decide whether to produce an upgrade of one of its programs. Customers would have to pay $100 for the upgrade. For the upgrade to be profitable, the company must sell it to more than 20% of their customers. You contact a random sample of 60 customers and find that 16 would be willing to pay$100 for the upgrade. Suppose that 30% of the company's customers would lea willing to pay $100 for the upgrade. The power of the test to detect this fact is 0.60. Interpret this value.

A software company is trying to decide whether to produce an upgrade of one of its programs. Customers would have to pay $100 for the upgrade. For the upgrade to be profitable, the company has to sell it to more than 20% of their customers. You contact a random sample of 60 customers and find that 16 would be willing to pay$100 for the upgrade. Which would be a more serious mistake in this setting-a Type I error or a Type II error? Justify your answer.

What were Stalin's motives in supporting Communist governments in Eastern Europe?

Consider the following problem.

One number is 3 less than 6 times a second number. Their sum is 46. Find the numbers.

If x represents the second number, which equation is correct for solving this problem?

A. $46-(x+3)=6x$

B. $(3-6x)+x=46$

C. $46-(3-6x)=x$

D. $(6x-3)+x=46$