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QNT 561 Week 2 Quiz

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 organizations symptoms, its problems, the managers 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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