1. The probability distribution shown here describes a population of measurements that can assume values of 1, 2, 3, and 4, each of which occurs with the same relative frequency.;x p(x);1 0.25;2 0.25;3 0.25;4 0.25;a. Calculate the mean of all the different samples of n=2 measurements that can be selected from this population. Select the correct choice below.;b. If a sample of n=2 measurements is randomly selected from the population, what is the probability that a specific sample will be selected?;c. Complete the sampling distribution table.;Construct a probability histogram for the sampling distribution of x.;2. Suppose a random sample of n=64 measurements is selected from a population with a mean? and standard deviation?. For each of the following values of? and? give the values of?- and?-;a.?=8?=2;b.?=64?=64;c.?=16?=56;d.?=8?=152;3. A random sample of n=100 observations is selected from a population with? =30 and?=22. Approximate the probabilities shown below.;a. P(x?28);b. P(22.1?x?26.8);c. P(x?28.2);d. P(x?27.0);4. A random sample of 93 observations produced a mean x=26.2 and a standard deviation s=2.4.;a. Find a 95% confidence interval for?.;b. The 90% confidence interval for?.;c. The 99% confidence interval for?.;5. The random sample shown below was selected from a normal distribution.;10,3,4,7,4,8;a. Construct a 95% confidence interval for the population mean?.;b. Assume that sample mean x and sample standard deviation remain exactly the same as those you just calculated but they are based on the sample of n=25 observations. Repeat part a. What is the effect of increasing the sample size on the width of the confidence interval?;6. For the binomial sample information summarized below indicate whether the sample size is large enough to use the large sample approximation to construct a confidence interval for p.;n=40, p=0.25;Is the sample size large enough?;7. A newspaper reported that 50% of people say that some coffee shops are overpriced. The source of this information was a telephone survey of 40 adults.;a. Identify the population of interest.;b. Identify the sample.;c. Identify the parameter of interest.;d. The 90% confidence interval for the parameter of interest;Question 8: If you wish to estimate a population mean with a sampling distribution error SE=0.29 using a 95% confidence interval and you know from prior sampling that?^2 is approximately equal to 4.1 how many observations would have to be included in your sample?;9. Suppose N=5,000, n=1,000, and s=50.;a. What is the standard error of x?;b. What is the standard error of x if n=2,000?;c. What is the standard error of x if n=5,000?;d. What happens to the standard error of x as n is increased?;10. Suppose you want to estimate a population proportion, p, and p^=0.33 and N=6,100, and n=1,400. Find an approximate 95% confidence interval for p.;11. What is specifically observed or what participants are asked in research study?;12. Data which someone has at least interpreted once since the event has occurred and has been recorded.;13. When a business decision is required in response to a problem or opportunity this is called.;14. Which characteristic of good research involves distinguishing between the organization?s symptoms, its problems, the manager?s perception of the problems, and the research problem?;15. Which of the following types of research is conducted to answer the questions who, what, where, and sometimes how?;16. This type of study is loosely structured and designed to understand future research requirements.;17. A firm is conducting a research study trying to ascertain if customers are sensitive to price changes on its products. This is an example of.
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