Sample annual salaries (in thousands of dollars) for employees at a company are listed.

$$\begin{array}{lllllllllllll}40 & 35 & 49 & 53 & 38 & 39 & 40 & 37 & 49 & 34 & 38 & 43 & 47\end{array}$$

(a) Find the sample mean and sample standard deviation. (b) Each employee in the sample is given a $\$ 1000$ raise. Find the sample mean and sample standard deviation for the revised data set. (c) Each employee in the sample takes a pay cut of $\$ 2000$ from their original salary. Find the sample mean and sample standard deviation for the revised data set. (d) What can you conclude from the results of (a), (b), and (c)?

Sample annual salaries (in thousands of dollars) for employees at a company are listed.

$$\begin{matrix} \text{40} & \text{35} & \text{49} & \text{53} & \text{38} & \text{39} & \text{40}\\ \text{37} & \text{49} & \text{34} & \text{38} & \text{43} & \text{47} & \text{35}\\ \end{matrix}$$

Each employee in the sample takes a pay cut of $2000 from their original salary. Find the sample mean and the sample standard deviation for the revised data set.

Sample annual salaries (in thousands of dollars) for employees at a company are listed.

$$\begin{matrix} \text{40} & \text{35} & \text{49} & \text{53} & \text{38} & \text{39} & \text{40}\\ \text{37} & \text{49} & \text{34} & \text{38} & \text{43} & \text{47} & \text{35}\\ \end{matrix}$$

Find the sample mean and the sample standard deviation.

In this exercise, we have given population data for a variable. For each exercise, do the following tasks.

a. Find the mean, $\mu$, of the variable.

b. For each of the possible sample sizes, construct a table and draw a dotplot for the sampling distribution of the sample mean.

c. Construct a graph and interpret your results.

d. For each of the possible sample sizes, find the probability that the sample mean will equal the population mean.

e. For each of the possible sample sizes, find the probability that the sampling error made in estimating the population mean by the sample mean will be 0.5 or less (in magnitude), that is, that the absolute value of the difference between the sample mean and the population mean is at most 0.5.

In this exercise, we have given population data for a variable. For each exercise, do the following tasks.

a. Find the mean, $\mu$, of the variable.

b. For each of the possible sample sizes, construct a table and draw a dotplot for the sampling distribution of the sample mean.

c. Construct a graph and interpret your results.

d. For each of the possible sample sizes, find the probability that the sample mean will equal the population mean.

e. For each of the possible sample sizes, find the probability that the sampling error made in estimating the population mean by the sample mean will be 0.5 or less (in magnitude), that is, that the absolute value of the difference between the sample mean and the population mean is at most 0.5.

Population data: 1,2,3.

Sample annual salaries (in thousands of dollars) for employees at a company are listed.

$$\begin{array}{lllllll} 40 & 35 & 49 & 53 & 38 & 39 & 40 \\ 37 & 49 & 34 & 38 & 43 & 47 & 35 \end{array}$$

What can you conclude from the results of the previous parts?

The English statistician Karl Pearson (1857–1936) introduced a formula for the skewness of a distribution.

$$P = \frac { 3 ( \overline { x } - \text { median } ) } { s }$$

Most distributions have an index of skewness between -3 and 3. When P > 0, the data are skewed right. When P < 0, the data are skewed left. When P = 0, the data are symmetric. Calculate the coefficient of skewness for each distribution. Describe the shape of each.(a)

$$\overline { x } = 17, s = 2.3, \text { median } = 19$$

(b)

$$\overline { x } = 32 , s = 5.1 , \text { median } = 25$$

(c)

$$\overline { x } = 9.2 , s = 1.8 , \text { median } = 9.2$$

(d)

$$\overline { x } = 42 , s = 6.0 , \text { median } = 40$$

Annual salary plus bonus data for chief executive officers are presented in the $BusinessWeek$ Annual Pay Survey. A preliminary sample showed that the standard deviation is $\$675$ with data provided in thousands of dollars. How many chief executive officers should be in a sample if we want to estimate the population mean annual salary plus bonus with a margin of error of $\$100,000$? (Note: The desired margin of error would be $E=100$ if the data are in thousands of dollars.) Use $95\%$ confidence.

Sample annual salaries (in thousands of dollars) for employees at a company are listed.

$$43, 46, 57, 47, 34, 34, 43, 46, 57, 32, 47, 43, 44$$

Find the sample mean and sample standard deviation.

Determine whether the numerical value is a parameter or a statistic. Explain your reasoning.

The average annual salary for the 43 employees of a company is 42,500 dollars.

Sample annual salaries (in thousands of dollars) for employees at a company are listed.

$$48, 45, 62, 59, 32, 32, 48, 45, 62, 26, 59, 48, 49.$$

To calculate the monthly salary, divide each original salary by $12$. Find the sample mean and sample standard deviation for the revised data set.

If a random sample of size 36 is obtained from a population with mean 50 and standard deviation 24, what is the mean and standard deviation of the sampling distribution of the sample mean?

Find the mean and standard deviation of the population. List all samples (with replacement) of the given size from that population and find the mean of each. Find the mean and standard deviation of the sampling distribution of sample means and compare them with the mean and standard deviation of the population. The numbers of DVDs rented by each of four families in the past month are 8, 4, 16, and 2. Use a sample size of 3.

Compute the mean and standard deviation for the following sample of $n=5$ scores: $70,72,71,80$, and 72. Hint: To simplify the arithmetic, you can subtract 70 points from each score to obtain a new sample. Then, compute the mean and standard deviation for the new sample. Finally, make the correction for having added 70 points to each score to find the mean and standard deviation for the original sample.

A population and sample size are given. (a) Find the mean and standard deviation of the population. (b) List all samples (with replacement) of the given size from the population and find the mean of each. (c) Find the mean and standard deviation of the sampling distribution of sample means and compare them with the mean and standard deviation of the population. The minutes of overtime reported by each of the three executives at a corporation are 90, 120, and 210. Use a sample size of 3.