In the 1980s, PepsiCo Inc., which then had 28 percent of the soft-drink market, proposed to acquire the Seven-Up Company. Shortly thereafter, the Coca-Cola Company, with 39 percent of the market, indicated it wanted to acquire the Dr Pepper Company. Seven-Up and Dr Pepper each controlled about 7 percent of the market. In your judgment, was the government’s decision to block these mergers appropriate?

Identify which of these types of sampling is used: random, systematic, convenience, stratified, or cluster. The author was an observer at a police sobriety checkpoint at which every 5th driver was stopped and interviewed. (He witnessed the arrest of a former student.)

(a) If the goal is to estimate the price of a particular brand of soft drink at various stores in your county, suggest several strata that might be relevant to choose the stores.

(b) Suggest a feasible sampling method (not necessarily one of the standard ones).

A population has a mean of 200 and a standard deviation of 50. A simple random sample of size 100 will be taken and the sample mean $\bar{x}$ will be used to estimate the population mean.

What does the sampling distribution of $\bar{x}$ show?

The Internal Revenue Service wants to sample $1000$ tax returns that were submitted last year to determine the percentage of returns that had a refund. Describe a sampling method that would be appropriate in this situation. Explain your reasoning.

A survey of 56 random people in a small town found that $14 \%$ drives convertibles year-round. What is the margin of sampling error? What is the likely interval that contains the percentage of the population that drives convertibles year-round?

Suppose that $X_{1}, X_{2}, \ldots, X_{25}$ are i.i.d. $N\left(\mu, \sigma^{2}\right)$, where $\mu=0$ and $\sigma=10$. Plot the sampling distributions of $\bar{X}$ and $\hat{\sigma}^{2}$.

Suppose a random sample of n measurements is selected from a population with mean

$$\mu = 100$$

and variance

$$\sigma ^ { 2 } = 100$$

For each of the following values of n , give the mean and standard deviation of the sampling distribution of the sample mean

$$\overline { x }$$

$$n = 500$$

Asked what the central limit theorem says, a student replies, "As you take larger and larger samples from a population, the variability of the sampling distribution of the sample mean decreases." Is the student right? Explain your answer.

Suppose a random sample of n measurements is selected from a population with mean

$$\mu = 100$$

and variance

$$\sigma ^ { 2 } = 100$$

For each of the following values of n , give the mean and standard deviation of the sampling distribution of the sample mean

$$\overline { x }$$

$$n = 50$$

Suppose that we will randomly select a sample of $64$ measurements from a population having a mean equal to $20$ and a standard deviation equal to $4.$

Find the mean and the standard deviation of the sampling distribution of the sample mean $\overline{x}.$

Asked what the central limit theorem says, a student replies, "As you take larger and larger samples from a population, the spread of the sampling distribution of the sample mean decreases." Is the student right? Explain your answer.

A company inspects products coming through its production process and rejects detected products. One-tenth of the items are rejected. If samples of 50 items are taken, what is the standard deviation of the mean of the sampling distribution of sample proportions?

Identify the sampling technique used, and discuss potential sources of bias (if any). Explain. Using random digit dialing, researchers call 1400 people and ask what obstacles (such as childcare) keep them from exercising.