# SCMA1000-04W15 ASSIGNMENT 2

August 30, 2017

Question
SCMA1000-04W15
1
ASSIGNMENT 2 (10%)
(Due: March 27th, 2015)
Topic: Confidence Interval for a population mean
Question 1 (Modified from Case Problem 2 Gulf Real Estate Properties, textbook page 366) (8 marks)
Scenario: Gulf Real Estate Properties, Inc., collects data on location, list price, sale price, and number
of days it takes to sell each unit. Each condominium is classified as Gulf View if it is located directly
on the Gulf of Mexico or No Gulf View if it is located on the by or a golf course, near but not on the
Gulf. Sample data are provided in the Excel file posted on the course website. Assume that the
population of number of days to sell of Gulf View condominiums is approximately normally
distributed.
a) Let ? be the population mean number of days to sell for Gulf View condominiums. Use Excel to
construct a 95% confidence interval for ?. Data are provided in the Data for Question 1 sheet. [3]
(Please read the Excel instruction part II page 10 or textbook pages 370-371)
b) Use the sample mean and the sample standard deviation obtained from the Excel outputs in part a)
to reconstruct a 95% confidence interval for ? using the formulas provided in chapter 8. Interpret
c) Assume that another sample will be collected and the branch manager requested estimate of the
mean number of days to sell of Gulf View condominiums with a margin of error of 10 days. Use
95% confidence level, how large should the sample size be? (use the sample standard deviation
obtained in part a) as the planning value for the population standard deviation.) [2]
Topic: Confidence Interval for a population proportion
Question 2 (Modified from question 59, textbook page 364) (5 marks)
Workers in several industries were surveyed to determine the proportion of workers who feel their
industry is understaffed. A sample of 250 workers in the health care sector is selected and 33% of the
respondents said they were understaffed.
a) Let p be the population proportion of workers in the health care sector who feel their industry is
understaffed. Create a 98% confidence interval for p? [3]
b) Assume that another survey will be conducted to estimate the population proportion of workers in the
health care section who feel their industry is understaffed. With 98% confidence level, how large
would the sample need to be to provide a margin of error of 5% or less? (use the sample proportion
(33%) as the planning value, p*) [2]
Topic: Hypothesis Test for a population mean
Question 3 (Modified from Case Problem 1 Quality Associates, Inc., textbook page 413) (5 marks)
Quality Associates, Inc., a consulting firm, advises its clients about sampling and statistical
procedures that can be used to control their manufacturing processes. A client wants to know whether
her company’s manufacturing process is operating satisfactorily. Since the design specification
indicated the mean for the manufacturing process should be 12, Quality Associates suggested that
random samples of 40 be taken periodically and the following hypothesis test be conducted:
Ho ? = 12
Ha ? ? 12
SCMA1000-04W15
2
If Ho is rejected, the process is not operating satisfactorily and corrective action should be taken to
eliminate the problem. The client took a sample of 40 items and this sample provided a sample mean
of 11.8 and a sample standard deviation of 0.24.
At the 5% significance level, conduct the hypothesis test to determine if corrective action is needed.
Provide the p-value for the test.
Topic: Comparing two population means (two independent samples)
Question 4 (Modified from question 42, textbook page 467) (6 marks)
Mutual funds are classified as Load or No-Load funds. Load funds require an investor to pay an
initial fee based on a percentage of the amount invested in the fund. The No-Load funds do not require
this initial fee. Some financial advisors argue that the Load mutual funds may be worth the extra fee
because these funds provide a higher mean rate of return than the No-Load mutual funds. A sample of
25 Load mutual funds and a sample of 25 No-Load mutual funds were selected. Data were collected
on the annual return for the funds over a five-year period.
The data are contained in the Data for Question 4 sheet in the Excel file.
a) Use Excel (t-Test: Two-Sample Assuming Unequal Variances) to conduct a hypothesis to determine
whether the Load mutual funds have a higher mean annual return than the No-Load mutual funds over
the five-year period. Given = 5%. [3]
(Please read the Excel instruction part II pages 19-20 or textbook page 476)
b) Use the results obtained in the Excel outputs in part a) to fill in the table below. [3]
Sample size
Sample Mean
Sample Standard Deviation
Use the information in this table to construct a 95% confidence interval for the difference between
the population mean returns of the two groups (use the number of degrees of freedom for the
t distribution as the one obtained in the Excel output from part a)).
Instruction:
? You can work in a group of two on this assignment or work on your own if you prefer. If you work in a
group of two, you both should work together on every question to understand how to do each step.
? The Excel file that contains data sets for this assignment is posted on the course website. (Please click
on the Assignment 2 tab.)
? Please use Excel to do question 1 part a) and question 4 part a). Submit your excel file or copy and
paste all the Excel outputs to a Word document to report; Please solve other questions and other parts
by hand, clearly show your work to get the full mark for each question. For all decimal results, please
keep three decimal places.
? You can submit your assignment at the beginning of the class on the due date or submit it online via
the Dropbox tool on the course website by 1:30 PM on the due date.

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