Section One
Assignment Data Sets collection
- For part 2, a file named “Assignment Data Sets”, containing the data sets for the questions, can be downloaded from the e-learning site vUWS. You should find and download the data set for your group.
- You should use Excel to carry out all calculations and statistical analyses. Students should consult the Excel handout which can be found on vUWS
- To complete this assignment, you must provide the Excel outputs for each of the questions in a report.
- Your assignment submitted must be typed and word-processed.
- The maximum number of pages for each submission is six (6), not including the cover page. No mark will be given if the number of pages exceeds the limit.
- The assignment is to be submitted online by the team leader before 5pm, the day after your tutorial in Week 13
- Any late assignments will be penalized 10% of the total mark per day
Page 2 of 3
Part 1 – 10 marks
Question 1 (3 + 2 = 5 marks)
A small independent general practice has three doctors. Dr Smith sees 40% of the patients, Dr Tran sees 30% and Dr Jackson sees the rest. Dr Smith requests blood tests on 5% of her patients, Dr Tran requests blood tests on 8% of his patients and Dr Jackson requests blood tests on 6% of her patients.
An auditor from the Australian Health Insurance Commission randomly selects a patient from the past week;
a) What is the probability that the selected patient had a blood test as a result of a visit to the general practice?
b) What is the probability that given the selected patient had a blood test as a result of a visit to the general practice; they were seen by Dr Smith?
Question 2 (2 + 3 = 5 marks)
The lifetime of a certain brand of light bulb is normally distributed, with a mean of 7500 hours and a standard deviation of 700 hours.
a) If the light bulbs carry a warranty for 6000 hours, what proportion of the bulbs will fail before the warranty expires?
b) The manufacturer replaces for free all bulbs that fail while under warranty. If they are willing to replace 2% of light bulbs that fail, what warranty should they offer?
Part 2 – 20 marks
The Minister of Industry and Trade is interested in the characteristics of local businesses. He decides to concentrate on businesses in the Parramatta CBD and the Sydney CBD. He employees a research company to survey 70 local businesses. This was carried out and the following variables recorded.
Column 1 Profit What was your profit?
Column 2 Type Is the business privately held, publicly traded or a franchise? (Private = 1, Public = 2, Franchise = 3)
Column 3 Employee How many employees work at your business?
Column 4 Age How old is the company (in years)?
Column 5 Location Where is the company? (1 = Parramatta CBD, 2 = Sydney CBD)
Page 3 of 3
Question 3 (5 marks)
Calculate a 95% confidence interval for the unknown population mean business age.
Question 4 (5 marks)
Test, at the 1% level of significance, whether the average business has more than 15 employees.
Question 5 (5 marks)
Test, at the 5% level of significance, whether the average profit in 2014 differs between businesses located in Parramatta CBD or located in Sydney CBD.
[You may assume that the unknown population standard deviations for Parramatta and Sydney businesses are equal]
QUESTION 6 (5 marks)
Test, at the 5% level of significance, whether location (Parramatta or Sydney CBD) of the business is related to type of business (privately held, publicly traded or franchise)?
NOTE: The data for Part 2 was randomly created for the sole purpose of this assignment. The data for Part 2 can be assumed to be normally distributed for all continuous variables Questions are attached below
Section Two
Question 1
A bag contains 7 red and 10 white balls. In how many ways 4 balls are selected if there are more than 2 red balls?
Question 2 (10 marks)
In your own words, differentiate the following statistical terminologies with some examples.
a. Population Parameter and Sample Statistic (2.5 marks)
b. Descriptive Statistics and Inferential Statistics (2.5 marks)
c. Nominal Scale and Ordinal Scale (2.5 marks)
d. Primary Data Source and Secondary Data Source (2.5 marks)
Week 3
Question 3 (10 marks)
Data showing the population by state in millions of people follow (The World Almanac, 2012). The
dataset in Excel file 2012Population.xlsx.
a. Develop a frequency distribution, a percent frequency distribution, and a histogram.
Use a class width of 2.5 million. (4 marks)
b. Does there appear to be any skewness in the distribution? Explain. (3 marks)
c. What observations can you make about the population of the 50 states? (3 marks)
Question 4 (10 marks) Forty-three percent of Americans use social media and other websites to voice their opinions about television programs (the Huffington Post, November 23, 2011). Below are the results of a survey of 1364 individuals who were asked if they use social media and other websites to voice their opinions about Television programs Uses Social Media and Other Websites to Voice Opinions About Television Programs Doesn’t Use Social Media and Other Websites to Voice Opinions About Television Programs Female 395 291 Male 323 355
a. Show a joint probability table. (2 marks)
b. What is the probability a respondent is female? (2 marks)
c. What is the conditional probability a respondent uses social media and other websites to voice opinions about television programs given the respondent is female? (3 marks)
d. Let F denote the event that the respondent is female and A denote the event that the respondent uses social media and other websites to voice opinions about television programs. Are events F and A independent?
Week 5 Question 5 (10 marks) The average starting salary for this year’s graduates at a large university (LU) is $20,000 with a standard deviation of $8,000. Furthermore, it is known that the starting salaries are normally distributed.
a. What is the probability that a randomly selected LU graduate will have a starting salary of at least $30,400?
b. What is the probability that a randomly selected LU graduate will have a salary of exactly $30,400? (2 marks)
c. Individuals with starting salaries of less than $15600 receive a low-income tax break. What percentage of the graduates will receive the tax break? (2 marks)
d. If 189 of the recent graduates have salaries of at least $32240, how many students graduated this year from this university? (3 marks)
Week 6 Question 6 (10 marks) The College Board reported the following mean scores for the three parts of the SAT (The World Almanac, 2009): Critical reading 502 Mathematics 515 Writing 494 Assume that the population standard deviation on each part of the test is 100.
a) What is the probability that a random sample of 90 test takers will provide a sample mean test score within 10 points of the population mean of 502 on the Critical reading part of the test? (4 marks)
b) What is the probability that a random sample of 90 test takers will provide a sample mean test score within 10 points of the population mean of 515 on the Mathematics part of the test? Compare this probability to the value computed in part (a).
Question 7
Binomial Distributions
Given your statistical knowledge, you have been asked to assist the quality control manager of a local manufacturer in establishing and seeing that the factory conforms to standards set by management. The facility manufactures a new electronic toy.
The factory can produce 1000 toys per day. Management has indicated that initially they will be satisfied if the defect rate is 3% or less.
Since you can’t quality-test every toy produced, you suggest that a random sample of 40 toys be taken. The results of testing 40 toys from today’s production line yields the results shown in the “WA3_Outcomes” Excel file Column 1.
Using Excel and this data:
- Create a pivot table.
- Analyze the result.
- Provide rationale relative to management’s target being met, your sample size of 40, and how representative the sample might be to the population.
Take a second sample of 40 toys. The results of this sample are shown in “WA3_Outcomes” Excel file Column 2.
- Create a pivot table for this sample.
- Analyze the result.
- Provide a rationale for how the knowledge gained from taking a second sample changes or does not change your analysis.
Since there are just two outcomes from the test, defective/not defective, you decide to utilize your knowledge of binomial probability distributions to assist the quality control manager in preparing a report for management.
- Using the Excel binomial distribution function, create a sampling distribution of the number of defects in each of many, many samples with the sample size of 40 and the target percent defective in the population equal to 3%.
- Analyze the result.
- Provide rationale relative to management’s target and your initial sample size of 40.
- Create a sampling distribution of the number of defects in each of many, many samples with the sample size of 200, but with the percent of defective toys you calculated in the second pivot table.
- Provide rationale relative to management’s target and your initial sample size of 40.
- How has the increase in the sample size changed your analysis?