Quantitative Analysis For Decision Making
Southern New Hampshire University
Quantitative Analysis For Decision Making
QSO 510
Midterm Take Home
Instructions
(ii) Show your approach to each question
(iii) To be submitted Next Tuesday
(iv) Please bring the hard copy of your midterm during our class meeting
(v) Brief notes are provided for each problem to help you figure out how to approach the questions
Problem 1
Auditors of Smart Spender Bank are interested in comparing the reported value of customer savings account balances with their own findings regarding the actual value of such assets. Rather than reviewing the records of each savings account at the bank, the auditors decide to examine a representative sample of savings account balances. The frame from which they will sample is shown below.
$75.30 $614.11 $696.34 $572.08 $748.23 $21.20
$99.79 $1,233.38 $530.40 $378.37 $596.14 $239.65
$2,995.38 $1,069.06 $929.80 $259.98 $123.65 $68.92
$192.35 $754.45 $309.00 $163.31 $71.75 $904.92
$40.70 $161.12 $459.38 $171.48 $402.81 $157.44
$41.81 $87.08 $489.97 $468.12 $400.57 $319.40
$533.82 $1,801.35 $1,666.50 $37.16 $85.92 $91.43
$193.14 $106.95 $214.62 $10.62 $582.18 $39.65
$123.66 $76.33 $291.73 $398.48 $659.18 $101.24
$1,740.47 $322.26 $1,509.34 $1,599.04 $358.62 $492.05
$1,052.68 $596.33 $100.54 $1,288.70 $421.46 $1,799.51
$581.21 $571.63 $180.58 $98.82 $358.68 $38.93
$874.78 $2,761.93 $750.44 $376.60 $269.48 $456.79
$216.81 $305.49
Notes; revise your notes to know what is population, frame, sampling units, etc. Also know steps in selecting random samples by using computer generated random values. Also, you need to know how to calculate summary measures of the population or a frame and samples then compare them to find sampling error and explain how good is a sample as a representation of the population or a frame (distribution)
Questions
(i) For these savings accounts, compute the mean score, the median and the standard deviation of the distribution
(ii) Use Excel to generate five simple random sample of size 25. Explain your approach
(iii) For each random sample you generated in (ii), calculate the mean scores, the medians and the standard deviations.
(iv) Find the sampling error for each sample.
(v) Find the mean of the means of the samples and compare it with the mean of the distribution (to get sampling error) and discuss your result
Problem 2
InnoSmart, the best Restaurant in town delivers food throughout the city of Manchvegas at no charge to the customers. However due to the company’s outstanding services, drivers are tipped by the customers handsomely. The owner of the restaurant is interested in estimating the mean tip income per delivery. To do this, he selected a simple random sample of 12 deliveries and recorded the tips that are received by the drivers. The following set of data is obtained (in $)
2.25 2.00 2.25 2.00 3.00 1.50 0.00 2.50 1.50 2.00 1.50 2.00
(a) Based on these sample data, what is the best point estimate to use as an estimate of the true mean tip delivery?
(b) Construct and interpret the 95% confidence interval estimate for the population mean
Problem 3
You are told that a random sample of 150 people from Manchester New Hampshire have been given cholesterol tests, and 60 of these people had levels over the “safe” count of 200.
Question
Construct a 95% confidence interval for the population proportion of people in Manchester New Hampshire with cholesterol levels over 200.
Note: Note that this question requires confidence interval for a proportion, the interval that is likely to capture the proportion of all population members’ that satisfy a specified property. Do you remember the formula? If not, here it is;
p estimate + – z-multiple X sqrt (p estimate (1-p estimate)/n)
Also note that, for population proportion, we use z-multiple not the t-multiple. So you can ask, where is the population standard deviation? You don’t need it. Look at the formula
Z-multiple in other words, it is z critical value, at the cutoff point.
Problem 4
InnoSmart fitness center in Manchvegas decided to carry out a study to measure the time its customers spent in the gym. The objective is to estimate the difference in mean time spent per visit for male and female customers. The company decided to hire you as a consultant to help in this exercise. You decided to start by collecting the sample data. You select a simple random samples of 100 males and 100 females at different times in the Gym and the resulting sample means are; Males: 34.5 minutes and Female: 42.4 minutes. You are informed that previous studies indicate that the standard deviation is 11 minutes for males and 16 for females. Develop a 95% confidence interval estimate for the difference in mean times following the following steps
(a) Identify population parameter or sample statistics of interest from the problem above
(b) Specify the desired confidence level
(c) Compute the point estimate
(d) Determine the critical value (the multiple)
(e) Determine the standard error of the sampling distribution
(f) Develop the confidence interval estimate using appropriate formula
(g) Provide a conclusion
Note: In class we discussed about the population parameters of interest. We mentioned among other things, the mean of population (single variable), population proportion, the difference between the means (remember the airport delay example which was shared in class), as well as the variance (standard deviation). So what do you think about the population parameter of interest in this question?
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