Homework Assignment (Week 3) – I602
This homework assignment contains 4 questions. Please provide a picture or electronic copy of
your procedures and answers for questions 1 and 2. If you do not have access to a tablet and a
stylus pen, you can provide a picture or a scanned copy of your answers. Please make sure your
solutions are clearly marked with question and part numbers and are completely legible. Your
procedure as well as your final answer will be marked. Therefore, please make sure to include your
complete procedure and the formulas you used in addition to your final answer.
Please provide your answers for Questions 3 and 4 directly in the Excel file "Week 3 – Excel".
Before submitting your solutions, please make sure all files can be opened without any errors.
Submit the file(s) for questions 1 and 2, along with the completed Excel file by uploading them
into the "Week 3 Homework Folder" folder on Avenue to Learn. You can find this folder under
Assessments>Assignments on the course webpage. The deadline for your submission is 11:59PM
on Sunday, October 16.
Question 1
As a manager you are interested in estimating how long it takes to complete a particular job. You
know that a sample average is a random variable, but knowing statistics, you would like to use the
sample average to estimate the population average using a confidence interval. You task your
assistant to collect a sample of observations on completion time of the job. He collects a sample
of 50 observations and reports that on average the job was completed in 14.72 hours. Assuming
the population standard deviation for the job completion time is 2 hours and assuming that
conditions are satisfied for a confidence interval,
(a) find the margin of error for a 95% confidence interval for the population mean.
(b) compute the 95% confidence interval for the population mean based on the information
provided.
Question 2
A survey of 200 randomly selected individuals at a shopping mall, indicated that 43% of families
used public transportation to come to the mall. You would like to use this information and estimate
the population proportion of mall visitors that use public transportation to come to the mall.
(a) What is the margin of error for a 90% confidence interval for the population proportion?
(b) What is the 95% confidence interval for the population proportion of mall goers that take
public transportation to come to the mall?
Prepared by: Dr. Behrouz Bakhtiari
Fall 2022
Note 1: Material required to answer Questions 3 and 4 using MS Excel are discussed in the
handout and topics in "Week 3" folder of Lecture Material on Avenue.
Note 2: In both questions, you are asked to find the upper and lower ends of a confidence
interval. Please note, you should use a method that will calculate every single part of the
confidence interval separately and then use them to find the upper and lower ends. This means,
you need to find your point estimate, your z or t value and each part of your standard error
separately, and then put them together to find the lower and upper bounds of your confidence
interval. The Excel sheet specifies where you need to place the formulas for your upper and
lower bounds. However, feel free to put the formulas for the other parts mentioned above in
any other neighboring cells, just like we did in the example solved in the handout. Use Excel
formulas for all parts of your formula.
Note 3: For the following two questions you may need to know the following Excel functions:
=COUNTA(range) : this function counts the number of data points in the range.
=COUNTIF(range, 5) : this function counts the number of times number 5 was repeated in
the specified range. Replace 5 by any other number to find the count of that number in the
range.
Question 3
An analyst is interested to find out if the average speed of cars on a certain portion of a road is
above 70 miles per hour (mph). She collects a sample of 40 cars passing through that portion of
the road and records their speed. The data is provided in the "Question 3" tab of the Excel file
"Week 3 – Excel".
(a) Using interval estimation techniques, provide the upper and lower bounds of a 90%
confidence interval for the population mean of average speed. See the notes above.
(b) Indicate, based on your results, if the average speed of cars in that portion of the road is
above 70 mph. Provide your answer in the text box provided (or add your own textbox to
enter your answer).
Question 4
You'd like to estimate the proportion of employees at a large firm who hold a line-of-credit using
a confidence interval. You collect a sample of 24 randomly selected employees and record if each
employee holds a line-of-credit. This data is stored in the "Question 4" tab of the Excel file "Week
3 – Excel". Please note, the value 0 means the employee does not hold a line-of-credit, and value
1 indicates they do. Using the data provided find the lower and upper bounds of a 99% confidence
interval for the population proportion of employees at this firm who hold a line-of-credit. See the
notes above.
Prepared by: Dr. Behrouz Bakhtiari
Fall 2022