The computer giant IBM has 329,373 employees and 637,133 stockholders. A vice president plans to conduct a survey to study the number of shares held by individual stockholders.

c. If the survey is conducted by telephoning 20 randomly selected stockholders in each of the 50 United States, what type of sampling (random, systematic, convenience, stratified, cluster) is being used?

The length of human pregnancies from conception to birth varies according to a distribution that is approximately Normal with mean 266 days and standard deviation 16 days. A study enrolls a random sample of 16 pregnant women.

(a) What are the mean and standard deviation of the sampling distribution ofx?

(b) What is the probability that the average pregnancy length exceeds 270 days?

Random samples of size n=500 were selected from a binomial population with p=.1. a. Is it appropriate to use the normal distribution to approximate the sampling distribution of $\hat{p}$? Check to make sure the necessary conditions are met. Using the results of part a, find these probabilities: b. $\hat{p}\gt$.12 c. $\hat{p}\lt$.10 d. $\hat{p}$ lies within .02 of p

The birth weights of males born full term are normally distributed with mean $\mu=3.4$ kilograms and standard deviation $\sigma=0.5$ kilogram. A large city hospital selects a random sample of 15 full-term males born in the last six months. Calculate the mean and standard deviation of the sampling distribution of $\bar{x}$ for SRSs of size 15.

A random sample is to be selected from a population that has a proportion of successes $\pi=0.65$. Determine the mean and standard deviation of the sampling distribution of p for each of the following sample sizes:

(a) $n=10 \quad 0.65,0.1508$

(b) $n=20 \quad 0.65,0.1067$

(c) $n=30 \quad 0.65,0.0871$

(d) $n=50 \quad 0.65,0.0675$

(e) $n=100 \quad 0.65,0.0477$

(f) $n=200 \quad 0.65,0.0337$

Suppose that we will randomly select a sample of $n$ elements from a population and that we will compute the sample proportion $\hat{p}$ of these elements that fall into a category of interest. If we consider the sampling distribution of $\hat{p}$. Write formulas that express the central tendency and variability of the population of all possible sample proportions. Explain what each of these formulas means in your own words.

Three professors examined awareness of four widely disseminated retirement rules among employees at the University of Utah. These rules provide simple answers to questions about retirement planning. At the time of the investigation, there were approximately 10,000 benefited employees, and 3,095 participated in the study. Demographic data collected on these 3,095 employees included gender, age (years), education level (years completed), marital status, household income ($), and employment category.

Describe the population of interest.

The list of individuals from which a sample is actually selected is called the sampling frame. Ideally, the frame should list every individual in the population, but in practice this is often difficult. A frame that leaves out part of the population is a common source of undercoverage.

(a) Suppose that a sample of households in a community is selected at random from the telephone directory. What households are omitted from this frame? What types of people do you think are likely to live in these households? These people will probably be underrepresented in the sample.

(b) It is usual in telephone surveys to use random-digit dialing equipment that selects the last four digits of a telephone number at random after being given the exchange (the first three digits). Which of the households you mentioned in your answer to (a) will be included in the sampling frame by random-digit dialing?

A box has two balls, one white and one red. We select one ball, put it back in the box, and select a second ball (sampling with replacement). Let $T$ be the event of getting the white ball twice, $F$ the event of picking the white ball first, and $S$ the event of picking the white ball in the second drawing.

Are $F$ and $S$ independent?

The ski patrol at Vail, Colorado, is studying slab avalanches in its region. A random sample of avalanches in spring gave the following thicknesses (in cm):

$$\begin{array}{ccccccc} 59 & 51 & 76 & 38 & 65 & 54 & 49 & 62 \\ 68 & 55 & 64 & 67 & 63 & 74 & 65 & 79 \end{array}$$

i. Use a calculator with mean and standard deviation keys to verify that $\bar{x} \approx 61.8$ and $s \approx 10.6 \mathrm{cm}$. ii. Assume the slab thickness has an approximately normal distribution. Use a 1% level of significance to test the claim that the mean slab thickness in the Vail region is different from that in Canada. What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. Compute the value of the sample test statistic.

In a recent election, a survey of randomly selected registered voters was conducted to determine which candidates was likely to win. 48% of respondents said that they would vote for candidate A, 46% said they would vote for candidate B, and 6% were undecided. Based on the sampling results, can you make a general conclusion that is more likely that candidate A will win the election? Explain.

If a population of raw scores is normally distributed and has a mean $\mu$ = 80 and a standard deviation $\sigma$ = 8, determine the parameters $\left(\mu_{\overline{X}} \text { and } \sigma_{\overline{X}}\right)$ of the sampling distribution of the mean for the following sample sizes. sample sizes. a. N = 16 b. N = 35 c. N = 50 d. Explain what happens as N gets larger

A box has two balls, one white and one red. We select one ball, put it back in the box, and select a second ball (sampling with replacement). Let $T$ be the event of getting the white ball twice, $F$ the event of picking the white ball first, and $S$ the event of picking the white ball in the second drawing.

Are $T$ and $F$ independent?.

The XYZ Corporation is interested in possible differences in days worked by salaried employees in three departments in the financial area. A survey of 23 randomly chosen employees reveals the data shown below. Because of the casual sampling methodology in this survey, the sample sizes are unequal. Research question: Are the mean annual attendance rates the same for employees in these three departments?