Applied Research and Statistics QNT561
Research and Sampling Designs
Shindeera Robinson
June 21, 2010

Chapter 8
21. What is sampling error? Could the value of the sampling error be zero? If it were zero, what would this mean? Sampling error is the difference between the statistic estimated from a sample and the true population statistic. While we would expect the sampling error to not be zero, it is not impossible. For example if you were evaluating the ethnicities of a population and everyone in the population was Caucasian then taking any sample would give you the true proportion of 100% Caucasian. In other words, if the sampling error is zero then the population is uniform or you were taking a perfectly representative sample

22. List the reasons for sampling. Give an example of each reason for sampling. A sample is a finite part of a statistical population whose properties are studied to gain information about the whole(Webster, 1985). When dealing with people, it can be defined as a set of respondents(people) selected from a larger population for the purpose of a survey. A population is a group of individuals persons, objects, or items from which samples are taken for measurement for example a population of presidents or professors, books or students

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? U=110,000 S=40,000 N= 50

SE = s/ sqrt (n) = 40000/ sqrt (50) = 5656.85425
The standard error of the mean is 5656.85425
B. What is the expected shape of the distribution of the sample mean? The expected shape of the sample mean will be the bell shaped curve, with the centered mean of 110,000 and a standard deviation of 5656.85 C. What is the likelihood of selecting a sample...

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QNT561 Final Exam
1) Which of the following measures of central location is affected most by extreme values? A. MeanB. MedianC. Mode D. Geometric mean
2) A correlation matrix…A.Shows all simple coefficients of correlation between variablesB. shows only correlations that are zeroC. shoes the correlations that are positiveD. shows only the correlations that are statistically significant
3) In a set of observations, which measure of central tendency reports the value that occurs most often? A. Mean B. MedianC. ModeD. Geometric mean
4) Which level of measurement is required for the median? A. Nominal B. OrdinalC. IntervalD. Ratio
5) The mean and the variance are equal in…A. the normal distributionB. the binomial distributionC. the Poisson distributionD. the hypergeometric distribution
6) The difference between the sample mean and the population mean is called the…A. margin of errorB. population standard deviationC. standard error of the meanD. sampling error
7) A dummy variable or indicator variable… A. may assume only a value of 0 or 1B. is another term for the dependent variableC. is a quantitative variableD. is a variable at a ratio or interval level of measurement
8) A Type I error is…A. the correct decisionB. a value determined from the test statisticC. rejecting the null hypothesis when it is trueD. accepting the...

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Name
Assignment
QNT/561
Date
Descriptive Statistics
Sales (in USD)
The distribution is normally distributed.
Central Tendency:
Mean = 42.84 dollars.
Dispersion:
Standard deviation = 9.073 dollars.
Count:
100
Min/Max:
Min is $23.00; Max is $64.00
Confidence Interval (alpha = 0.05):
$41.06 to $44.62
The histogram is present in Appendix A; the descriptive statistics are present in Appendix B.
Age
The distribution is not normally distributed.
Central Tendency:
Median = 35 years
Dispersion:
Interquartile Range = 12 years / 2 = ± 6 years
Count:
100
Min/Max:
Min is 25 years; Max is 45 years
Confidence Interval:
The data is not normally distributed, therefore there is no confidence interval
The histogram is present in Appendix A; the descriptive statistics are present in Appendix B; the scatterplot relating age and sales is in Appendix C.
ID On Display
Thirty-four percent of the people sampled did not have their ID on display while sixty-six percent of people sampled had their ID on display. The bar chart is in Appendix E.
Descriptive Statistics Interpretation
Sales
One hundred people were randomly selected, and their sales were measured. Their sales were observed between $23.00 and $64.00. The average sales were $42.84, with a standard deviation of $9.07. Approximately half or more of the data values are above $42.84. There is enough evidence to say that the...

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Week 1
Assignments:
QNT561 Week 1 Practice Problems
Chapter 2 and 4
Name
QNT561
June 18, 2012
Debasis Bhattacharya
Chapter 2 answers
2.37
Sample mean = (3.2+2.5+2.1+3.7+2.8+2.0)/6 = 16.3/6 = 2.717
The median is the middle value when the data set is ordered.
Here since we have even number of observations we need to find the average of the two middle values.
Ordered data: 2.0, 2.1, 2.5, 2.8, 3.2, 3.7
Median = (2.5+2.8)/2 = 2.65
2.38
a. Mean = Sum/n = 85/10 = 8.5
b. Mean = Sum/n = 400/16 = 25
c. Mean = Sum/n = 35/45 = 0.778
d. Mean = Sum/n = 242/18 = 13.444
Week 1 Dq1:
How may variance and standard deviation be applied to a real-world business-related problem? Provide a specific application in which these measures are useful.
Week 1 Dq2
When would you use Chebyshev’s theorem and the empirical rule in business? How are they...

...clarification if something is unclear. In personal interview the participant can be prescreened to ensure that he/she fits the population profile being surveyed. The disadvantage of personal interview is that is has high costs and there is need for trained interviewer, it takes longer time to collect data and follow up is harder and also some participants might be unwilling to talk and could be harder to reach.
e) A local college has been provided a new work-study grant to assist with the high cost of tuition. It has 4500 students currently enrolled and has potentially 1500 eligible to submit applications for this new grant money. It needs a study of applicant requirements, job tasks and performance expectations as part of the grant research follow-up study.
In this case the self-administered questionnaire would be the best case, because there is a large number of students to be surveyed and it would be easier to administer. It looks like there would be large number of questions that would need to be completed and thus sending the questionnaire to students via mail to fill them out and return them would be the most efficient option. This is quick and economical method for distributing questionnaire to a large number of students spread over the area. It will give respondents a feeling of confidentiality and anonymity and it will allow them time to complete the questionnaire in their respondents convenience. It is important that design of the questions in...

...Running head: BUSINESSRESEARCH METHODS PART III
BusinessResearch Methods Part III
University of Phoenix
AppliedBusinessResearch and Statistics561
March 29, 2010
BusinessResearch Methods Part III
Team C’s BusinessResearch Methods Part I analysis determined a problem within Toyota Motor Corporation’s recent recalls that posed a potential for decreased customer satisfaction, which has the additional potential for impacting sales. Part II proposed a sample design and appropriate collection methods, a sample survey, a presentation, and classification of findings. In Part III, the final piece of this essay, the statistical analysis from Part II will be discussed as well as the potential challenges and validity of the original research question and the data analysis that followed. Finally, the findings are presented in the proper response type, and classified in order of power in appendix A. The research question Team C proposed is “Is there a statistically significant relationship between customer satisfaction and Toyota sales in the U.S.?”
Statistical Analysis
The previous data in Part II concluded that in Toyota’s 2009 fiscal year, the company sold 2.21 million units. Although the 2010 fiscal year is not yet complete, the company has sold 1,567,006...

...Central Limit Theorem and Confidence Intervals Problem Sets
Tiffany Blount
QNT561
September 7, 2010
Michelle Barnet
University of Phoenix
Central Limit Theorem and Confidence Intervals Problem Sets
Chapter 8 Exercises:
21. What is sampling error? Could the value of the sampling error be zero? If it were zero, what would this mean?
* Sampling error is the difference between the statistic estimated from a sample and the true population statistic. It is not impossible for the sampling error to not be zero. If the sampling error is zero then the population is uniform. For example if I were evaluating the ethnicities of a populations and everyone is the population was Black then taking any sample would give me the true proportion of 100% Black.
22. List the reasons for sampling. Give an example of each reason for sampling.
* The population size is too large and costly for making the study feasible in reasonable period.
For example, if I want to know how watching the violent shows on television affects the behavior of children, it won’t be realistic to study each child in the population, so I would use sampling.
* Only estimation of particular section of population is required
For example, if I want to take an example of nation which is combined unit of states. I can choose the random samples of states which can be further divided into smaller units like cities. These cities can be...

...Chapt 10 # 42
H0: game length is >= 3.5 hours
Ha: game length is < 3.5 hours
mean = 2.9553
stdev = 0.5596
Get the t test statistic:
t = (x-mu)/(stdev/sqrt(N))
t = (2.9553-3.5)/(0.5596/sqrt(17))
t = -4.0133
Get the critical value for df = N-1 = 16, one tail, alpha is 0.05:
-1.7459
Since our test statistic is much lower than the critical value, we reject the null hypothesis. There is enough evidence to conclude that games are shorter than 3.50 hours.
Chapt 11 # 58
The amount of income spent on housing is an important component of the cost of living. The total costs of housing for homeowners might include mortgage payments, property taxes, and utility costs (water, heat, electricity). An economist selected a sample of 20 homeowners in New England and then calculated these total housing costs as a percent of monthly income, five years ago and now. The information is reported below. Is it reasonable to conclude the percent is less now than five years ago?
Home Owner Five years ago Now
1 17% 10%
2 20 39
3 29 37
4 43 27
5 36 12
6 43 41
7 45 24
8 19 26
9 49 28
10 49 26
11 35% 32%
12 16 32
13 23 21
14 33 12
15 44 40
16 44 42
17 28 22
18 29 19
19 39 35
20 22 12
SOLUTION
Before After
1 17 10
2 20 39
3 29 37
4 43 27
5 36 12
6 43 41
7 45 24
8 19 26...

...Null Hypothesis:Ho: p = 50.%
Alternative Hypothesis:H1: p > 50.%
Level of significance=alpha (a) = 0.10 or 10.0%
This is a one tailed test because we are testing the area in the right tail
Since the sample size is large we will use z distribution
z critical= 1.2816
Decision rule
If the sample z value > z critical, 1.2816 reject Null Hypothesis
If the sample z value < z critical , 1.2816 accept Null Hypothesis
Alternatively:
If p value < significance level , 0.1 reject Null Hypothesis
If p value > significance level , 0.1 Accept Null Hypothesis
Decision rule: If the area in the right tails is less than the level of significance (0.10 0r 10%) reject the Null Hypothesis
Or alternatively z statistic computed for the sample should be lesser than z corresponding to 10% significance level
p= 50.00%
q= 50.00%
n= 60
sp=standard error of proportion=square root of (pq/n)= 6.4550% =square root of ( 50.% * 50.% / 60)
sample proportion= 63.33% =38/60
z=(sample proportion-population proportion)/ standard error= 2.0651 =(63.33%-50.%)/6.455%
P-value:
This is a one tailed test therefore area in one of the tails is checked
Cumulative probability corresponding to the obtained z value of 2.0651 is 98.05%
Thus the area in the right tail= 1.95% =100% -98.05%
P-value= 1.95%
For the null hypothesis to hold the area in the right tail should at least be greater than 10.00%
Since this condition is not...

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