21. What is a sampling error Could the value of the sampling error be zero If it were 0, what would this mean A sampling error is the difference between a sample statistic and its corresponding population parameter. Yes, if one were to determine the sum of these sampling errors over large numbers of samples the result would be very close to zero. This is true because the sample mean is an unbiased estimator of the population mean.
22. Lists the reasons for sampling. Give an example for each reason for sampling. 1. It would not be feasible or practical to contact an entire population. 2. It would be cost prohibitive to study an entire population. 3. It would be physically impossible to check all items in the population. 4. Due to the destructive nature of some tests. 5. Sample results are adequate.
34. Information from the American Institute of Insurance indicates the mean amount of life
insurance per household in the United States is $110,000. This distribution follows the
normal distribution with a standard deviation of $40,000.
a. If we select a random sample of 50 households, what is the standard error of the mean= 40000/square root of 50=5656.85
b. What is the expected shape of the distribution of the sample mean-normal
c. What is the likelihood of selecting a sample with a mean of at least $112,000= P(mean)=112000)=P(z>(112000-110000)/5656.85)=P(z>=.3536=1-P(z<.3536)=.3618 d. What is the likelihood of selecting a sample with a mean of more than $100,000= P(Mean > 100000) = P(z > (100000-110000)/5656.85)
= P(z>- 1.768) = 1 ??“ P(z<- 1.768) = 0.9615 e. Find the likelihood of selecting a sample with a mean of more than $100,000 but less than $112,000.= P(100000 < sample mean < 112000) = P(sample mean > 100000) ??“ P(sample mean >= 112000) = 0.9615 ??“ 0.3618 = 0.5997.
Chapter 9 32,34,36
32. A state meat inspector in Iowa has been given the assignment of estimating the mean
net weight of packages of ground chuck labeled ???3 pounds.??? Of course, he realizes that
the weights cannot be precisely 3 pounds. A sample of 36 packages reveals the mean
weight to be 3.01 pounds, with a standard deviation of 0.03 pounds.
a. What is the estimated population mean= Estimated population mean = sample mean = 3.01 pounds
b. Determine a 95 percent confidence interval for the population mean.= 3.01-1.96*.03/square root 36, 3.01+1.96* .03/square root of 36= (3.0002, 3.0198)
34. A recent survey of 50 executives who were laid off from their previous position revealed
it took a mean of 26 weeks for them to find another position. The standard deviation of
the sample was 6.2 weeks. Construct a 95 percent confidence interval for the population
mean. Is it reasonable that the population mean is 28 weeks Justify your answer.
(26-1.96*6.2/square root of 50, 26+1.96*6.2/square root of 50=24.281, 27.719. Therefore, no it is not reasonable that the population mean is 28 weeks, because it is not even in the confidence interval.
36. The American Restaurant Association collected information on the number of meals eaten
outside the home per week by young married couples. A survey of 60 couples showed
the sample mean number of meals eaten outside the home was 2.76 meals per week,
with a standard deviation of 0.75 meals per week. Construct a 97 percent confidence
interval for the population mean.
Standard deviation= .7500
Standard error= .750/60squared
Right side= 3.236536
Z values are -2.1701 to 2.1701
98% confidence level is 2.283464 to 3.236536
Chapter 3 #5
5. You have been approached by the editor of Gentelmens magazine to carry out a research study. The magazine has been unsuccessful in attracting shoe manufactures as advertisers. When the sales force tries to secure advertising from shoe manufactures they were told mens clothing stores are a small dying segment of their business, since Gentlemens magazine goes chiefly to mens clothing stores, the manufactures reasoned that it was therefore, not a good vehicle for their advertising. The editor believes that a survey (via mail questionnaire) of mens clothing stores in the United States will probably show that these stores are important outlets for mens shoes and are not declining in importance as shoe outlets. Develop a proposal for the study and submit it to him. Develop the management research hierarchy that will help you to develop a specific proposal.
According to the text, the management research hierarchy is:
1. What are the symptoms that cause management concern What environmental stimuli raise management interest. In this case, I believe the symptoms are the loss in revenue from the shoe manufactures.
2. How can management eliminate the negative symptoms How can management fully capitalize on an opportunity In this case, in order to eliminate the loss in sales, one must show the shoe manufactures that mens clothing stores in the United States are important outlets for mens shoes and are not declining in importance as shoe outlets. They can capitalize on the opportunity by showing in numbers the sales of shoes, and not only getting the manufactures to advertise again, but to advertise heavily.
3. What plausible courses of action are available to management to correct the problem or take advantage of the opportunity, and which should be considered. This is where you can develop different courses of action to take. This is where different solutions to the dilemma are brainstormed. Such as give a higher commission to sales people, lower rates to the manufactures, etc.
4. What does the manager need to know to choose the best alternative from the available courses of action. This will be when you think of things that will happen if you implement things from #3
5. What should be asked/observed to obtain the information the manager needs This is where on the survey you list your questions.
6. What is the recommended course of action, given the research findings
What do we want to achieve How can we achieve these goals Then ask why the issue/problem/dilemma is happening. Things that can be done to ask these questions are by the use of surveys, use of secondary research, and additional study into the matter.
One should develop research questions that will help determine what can/should be done about the declining of advertising sales from shoe manufactures. Then one would use investigative questions to find out the possible reasons for the declining advertising sales. One needs to decide the method, technique to conduct the study. For instance, if one selects a survey, will it be mailed, done by computer, by phone, etc