A random sample of individuals were rated as to their standing posture. In addition, the numbers of days of back pain each had experienced during the past year were also recorded. Surprisingly to the researcher these data indicated a positive correlation between good posture and number of days of back pain. Does this indicate that good posture causes back pain?

What is your impression of this poem?

Identify the population, the parameter, the sample, and the statistic in each setting. From a large group of people who signed a card saying they intended to quit smoking, 1000 people were selected at random. It turned out that 210 (21%) of these individuals had not smoked over the past 6 months.

a. What causes osteoporosis? b. What factors increase a person's chances of getting osteoporosis? c. What can help prevent the development of osteoporosis?

Your grandfather complains of pain in his swollen and inflamed big toe and the doctor indicates that it is caused by gout. (a) How would you explain to him what gout is and its biochemical cause? (b) What can you suggest to him to prevent these gouty attacks?

Why did the economic problems in some EU countries have such a widespread impact?

Suppose Fuzzy, a quantum-mechanical duck, lives in a world in which $h=2 \pi \mathrm{J} \cdot \mathrm{s}$. Fuzzy has a mass of 2.0 kg and is initially known to be within a region 1.0 m wide.

Draw a line under each indefinite pronoun and circle each demonstrative pronoun. Everybody wants a copy of Taylor Joyce's newest novel.

An agreement among nations to stop a particular behavior is sometimes called a[n] _____. Explain why the word catapult would use the "to put down" form of cata-. Repeat the process for the word catalog.

Solve the given differential equation by using an appropriate substitution. $y^{\prime}+y \ln y=y e^{x}$

A computationally efficient way to compute the sample mean and sample variance of the data set $x_{1}, x_{2}, \ldots, x_{n}$ is as follows. Let $\bar{x}_{j}=\frac{\sum_{i=1}^{j} x_{i}}{j}, \quad j=1, \ldots, n$ be the sample mean of the first j data values, and let $s_{j}^{2}=\frac{\sum_{i=1}^{j}\left(x_{i}-\bar{x}_{j}\right)^{2}}{j-1}, \quad j=2, \ldots, n$ be the sample variance of the first $j, j \geq 2$ values. Then, with $s_{1}^{2}=0,$ it can be shown that $\bar{x}_{j+1}=\bar{x}_{j}+\frac{x_{j+1}-\bar{x}_{j}}{j+1}$ and $s_{j+1}^{2}=\left(1-\frac{1}{j}\right) s_{j}^{2}+(j+1)\left(\bar{x}_{j+1}-\bar{x}_{j}\right)^{2}$ (a) Use the preceding formulas to compute the sample mean and sample variance of the data values 3, 4, 7, 2, 9, 6. (b) Verify your results in part (a) by computing as usual. (c) Verify the formula given above for $\bar{x}_{j+1}$ in terms of $\bar{x}_{j}$.

Find possible choices for outer and inner functions f and g such that the given function h equals $f \circ g$. $h(x)=\sqrt{x^{4}+2}$

The following table gives the number of pedestrians, classified according to age group and sex, killed in fatal road accidents in England in 1922. (a) Approximate the sample means of the ages of the males. (b) Approximate the sample means of the ages of the females. (c) Approximate the quartiles of the males killed. (d) Approximate the quartiles of the females killed.

$$\begin{matrix} \text{Age} & \text{Number of Males} & \text{Number of Females}\\ \text{0-5} & \text{120} & \text{67}\\ \text{5-10} & \text{184} & \text{120}\\ \text{10-15} & \text{44} & \text{22}\\ \text{15-20} & \text{24} & \text{15}\\ \text{20-30} & \text{23} & \text{25}\\ \text{30-40} & \text{50} & \text{22}\\ \text{40-50} & \text{60} & \text{40}\\ \text{50-60} & \text{102} & \text{76}\\ \text{60-70} & \text{167} & \text{104}\\ \text{70-80} & \text{150} & \text{90}\\ \text{80-100} & \text{49} & \text{27}\\ \end{matrix}$$

The sample mean of the weights of the adult women of town A is larger than the sample mean of the weights of the adult women of town B. Moreover, the sample mean of the weights of the adult men of town A is larger than the sample mean of the weights of the adult men of town B. Can we conclude that the sample mean of the weights of the adults of town A is larger than the sample mean of the weights of the adults of town B? Explain your answer.