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Question 1 (8 marks) The Australian divorce rate has been steadily increasing over the years until late 1990s. However, data suggests that the rate has fallen in the most recent years. Age specific Australian divorce rates (in percentages) of male and female for few years between 1992 and 2012 are given in the attached Excel file (GB513Assignment-Q1.xls ). Using the information given in the data file, complete following tasks. a. Use a graphical technique to compare the divorce rates in 1992, 2008 and 2012 broken down by age for Australian Male. Describe your graph. (3 marks) b. Use a graphical technique to compare the divorce rates in 1992, 2008 and 2012 broken down by age for Australian Female. Describe your graph. (3 marks) c. Compare your observations in parts (a) and (b) above to comment on the differences in divorce rate for male and female over the years. (2 marks) Page 2 of 4 Question 2 (7 marks) The Australian Bureau of Statistics recently released figures on petrol usage. Following are the 15 leading cities in 2012. City value ($ billions) Bourke 7.84 Mt Isa 6.48 Weipa 4.20 Newcastle 4.17 Wollongong 4.00 Kalgoorlie 3.30 Darwin 3.21 Tennant Creek 2.74 Broken Hill 2.08 Perth 2.05 Alice Springs 2.05 Adelaide 1.89 Canberra 1.85 Dubbo 1.81 Albury 1.68 (a) Using the Data Analysis Tool in Excel, calculate the descriptive statistics. (2 marks) (b) Briefly explain what each of the metrics in the summary statistics means. (3 marks) (c) Comment on the figures in the report. What are they telling you about this data set? Is it symmetrical, flat, skewed, does it have outliers, and so on? (2 marks) Question 3 (5 marks) A popular media poll revealed that 44% of Australian adults in the 18-34 years category think that ‘Made in Australia’ ads boost sales. A different interactive poll showed that 78% of Australian adults in the 18–34 years category use social media. Suppose that 85% of Australian adults in the 18-34 years category think that ‘Made in Australia’ ads boost sales or use social media. If an Australian adult in the 18-34 years category is randomly selected: (a) What is the probability that the person thinks that ‘Made in Australia’ ads boost sales and uses social media? (2 marks) (b) What is the probability that the person thinks that ‘Made in Australia’ ads boost sales given that the person does not use social media? (3 marks) Please be sure to include all workings with your answers. Question 4 (10 marks) The proportion of credit-card holders who pay their bill in full each month is 20%; the other 80% make only a partial or no payment. (a) In a random sample of 17 customers, what is the probability that: i. 4 customers pay their bill in full? (3 marks) ii. More than 4 customers pay their bill in full? (3 marks) (b) What is the expected number of customers who credit card bill in full? (2 marks) (c) What is the standard deviation? (2 marks) Question 5 (10 marks) The number of calls received by a phone operator at an emergency department between 10-11am has a Poisson distribution with a mean of 12. (a) Find the probability that the operator received at least 5 calls during the following period. I. 10-11am (2 marks) II. 10-10.30am (2 marks) III. 10-10.15am (2 marks) (b) What is the probability that fever than 4 calls were received between 10 & 10.30am? (2 marks) (c) What is the probability that 6 or more calls were received between 10 & 10.30am? (2 marks) Question 6 (10 marks) According to a recent research report, the average monthly household mobile phone bill is $73. Suppose monthly household mobile phone bills are normally distributed with a standard deviation of $11.35. (a) What is the probability that a randomly selected monthly mobile phone bill is no more than $55? (2 marks) (b) What is the probability that a randomly selected monthly mobile phone bill is more than $100? (2 marks) (c) What is the probability that a randomly selected monthly mobile phone bill is between $80 and $90? (2 marks) (d) What is the probability that the average mobile phone bill of randomly selected sample of 25 bills is between $71 and $80? (4 marks) Please be sure to include all workings with your answers. Question 7 (10 marks) Suppose a study reports that the average price for a kilogram of grapes is $3.16. You believe that the price is higher in your area of the country. You decide to test this claim by randomly calling grocery stores. Your random survey of 25 stores produces the following prices (all in $). Assume grape prices for a region are normally distributed. Does the data you obtained provide enough evidence to support your belief? Conduct a hypothesis test at 1% level of significance and clearly state your conclusion. 3.27 3.29 3.16 3.20 3.37 3.20 3.23 3.19 3.20 3.24 3.16 3.07 3.27 3.09 3.35 3.15 3.23 3.14 3.05 3.35 3.21 3.14 3.14 3.07 3.10 Page 4 of 4 Note: You will need to explain how you determined the answer to the question. Submitting answers without an explanation for this question is not sufficient. End of Assessment
Access the University of Phoenix Material, "Data for Inferential Practice Problems." Use the Excel® Analysis ToolPak? when necessary for the following:
Develop a 95% confidence interval of the difference between the daily population means for the two airports.
The American Sugar Producers Association wants to estimate the mean yearly sugar consumption. A sample of 16 people reveals the mean yearly consumption to be 60 pounds with a standard deviation of 20 pounds.
What is the probability that both funds will exceed their respective benchmarks and the bookies give 2:1 odds that the NFC will win the Super bowl. What is the probability that the market will rise for the upcoming year
A local group claims that the police issue more than 60 speeding tickets a day in their area.
If Z = 1.96, s = 3, and E = 1, determine the correct sample size.
If an employee is selected for promotion, find the probability that the employee will be under 25 or a female. Express your answer as a fraction in lowest terms.
The number of stereos sold on each weekday. State the hypotheses and identify the claim, find the critical value(s), compute the test value, make the decision and summarize the results.
Frequent checks of unfilled orders at end of day reveal that distribution of unfilled orders follows Poisson distribution with mean of two orders. Sketch the histogram representing Poisson probability distribution of unfilled orders.
The rockets are playing Lakers tonight in basketball. The lakers average 90 points a game, with a SD of 10. What would the rockets need to score to be 80% sure of victory, 90% sure, 95% sure.
Does this sample show sufficient evidence that the private university loan default rate is below the rate for all universities, using a left-tailed = .01. That is, do you reject the null hypothesis?
For a candidate to win in a congressional district, he has to have won over half of the vote. The Republican candidate takes a poll to assess his chances in a two-candidate race.
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