REQUIRED: Answer questions 1 - 10 based on the following information
In recent times it has been suggested that university graduates can be divided into two groups, those who graduated from a business degree and those who did not. Suppose you are working for the Government and have been asked to determine whether this is the case. Of particular importance is the income of a graduate in their first year of employment. It is believed that higher incomes are more likely to be experienced by students who are not business graduates. Below is a statistical summary of a sample of incomes of non-business and business graduates (measured in $000s):
QUESTION ONE
According to the relative positions of the mean and median, what can you conclude about the skewness of the Business graduate incomes?
(a) Infinitely skewed
(b) No skewness (symmetrical)
(c) Negatively skewed
(d) Positively skewed
(e) None of the above
QUESTION TWO
What is the coefficient of variation of the Business graduate incomes?
(a) approximately 15%
(b) approximately 662%
(c) approximately 19%
(d) approximately 517%
(e) None of the above
QUESTION THREE
What is the coefficient of variation of the Non-Business graduate incomes?
(a) approximately 662%
(b) approximately 517%
(c) approximately 19%
(d) approximately 15%
(e) None of the above
QUESTION FOUR
What can be concluded by comparing these statistics?
(a) The Business graduates experience higher relative income variability than the Non-business graduates
(b) The Non-business graduates experience higher relative income variability than the Business graduates
(c) The Business graduates have the same relative income variability as the Non-business graduates
(d) The Business and Non-business graduates have zero relative income variability
(e) None of the above
QUESTION FIVE
What is the Interquartile Range of the Non-Business and Business graduates respectively?
(a) Non-Business graduates: 49 Business graduates: 22
(b) Non-Business graduates: 13 Business graduates: 6
(c) Non-Business graduates: 29 Business graduates: 9
(d) Non-Business graduates: 7 Business graduates: 7
(e) None of the above
QUESTION SIX
Select the most appropriate statement regarding the Coefficient of Variation (CV):
(a) The CV measures relative variation, i.e. Shows variation relative to the mean
(b) The CV can be used to compare two or more sets of data measured in different units
(c) The CV is always expressed as a percentage (%)
(d) All of the above
(e) None of the above
QUESTION SEVEN
If there are outliers in the data, what is the most appropriate measure of central tendency?
(a) Mean
(b) Mode
(c) Interquartile Range
(d) Median
(e) None of the above
QUESTION EIGHT
Are there outliers in the Business graduate incomes? If so, are they positive or negative?
(a) Yes there are outliers. They are positive
(b) No there are no outliers
(c) Not enough information
(d) Yes there are outliers. They are negative
(e) None of the above
QUESTION NINE
If there are outliers, how did you detect them?
(a) The mean is less than the median. This indicates positive outliers
(b) The mean is greater than the median. This indicates positive outliers
(c) The mean is greater than the median. This indicates negative outliers
(d) The mean is less than the median. This indicates negative outliers
(e) None of the above
QUESTION TEN
Select the most appropriate comparison between Business and Non-Business graduates:
(a) Business graduates earn higher incomes and have greater relative income variability
(b) Business graduates earn lower incomes and have greater relative income variability
(c) Business graduates earn lower incomes and have lower relative income variability
(d) Business graduates earn higher incomes and have lower relative income variability
(e) None of the above
REQUIRED: Answer questions 11 - 16 based on the following information
A university claims that the average tertiary entry (TE) score of applicants to its business studies program has increased during the past three years. Three years ago, the mean and the standard deviation of TE scores of the university's business studies program applicants were 920 and 20, respectively. In a sample of 36 of this year's applicants for the program, the mean TE score was 925. At the 5% level of significance, can we conclude that the university's claim is true?
QUESTION ELEVEN
What is the null and alternative hypothesis for this test?
(a) H0: µ ≥ 920, H1: µ <920
(b) H0: µ ≤ 920, H1: µ >920
(c) H0: µ = 920, H1: µ ≠ 920
(d) H0: µ ≠ 920, H1: µ = 920
(e) H0: µ ≤ 925, H1: µ >925
QUESTION TWELVE
What is (are) the critical value(s)?
(a) -1.96 and 1.96
(b) -1.645
(c) -1.645 and 1.645
(d) 1.645
(e) None of the above
QUESTION THIRTEEN
What is the calculated test statistic?
(a) approximately -1.5
(b) approximately -2.5
(c) approximately 0.5
(d) approximately 1.5
(e) None of the above
QUESTION FOURTEEN
What is your conclusion? (Choose the most correct answer)
(a) Accept H0 at the 1% level of significance
(b) Do not reject H0 at the 5% level of significance
(c) Reject H0 at the 5% level of significance
(d) Accept H1 at the 1% level of significance
(e) None of the above
QUESTION FIFTEEN
Calculate the p-value
(a) 0.9332
(b) 1.0668
(c) 0.0143
(d) 0.0668
(e) None of the above
QUESTION SIXTEEN
Interpret the meaning of the p-value
(a) The probability of observing a test statistic more extreme than the observed sample value given the null hypothesis is true.
(b) The observed level of significance.
(c) The smallest value of α for which H0 can be rejected.
(d) All of the above
(e) None of the above
REQUIRED: Answer questions 17 - 20 based on the following information
A certain type of orange seed germinates 90% of the time. A farmer planted 15 seeds.
QUESTION SEVENTEEN
What is the probability that exactly 13 germinate?
(a) approximately 0.345
(b) approximately 0.189
(c) approximately 0.267
(d) approximately 0.875
(e) None of the above
QUESTION EIGHTEEN
What is the probability that 13 or more germinate?
(a) 0.1840
(b) 0.8389
(c) 0.7242
(d) 0.8160
(e) None of the above
QUESTION NINETEEN
What is the expected number of seeds that germinate?
(a) Approximately 12
(b) Approximately 14
(c) Approximately 11
(d) Approximately 15
(e) None of the above
QUESTION TWENTY
What is the probability that none of the seeds germinate?
(a) Approximately 0.00
(b) Approximately 0.64
(c) Approximately 0.12
(d) Approximately 0.24
(e) None of the above
REQUIRED: Answer questions 21 - 25 based on the following information
The amount of time devoted to studying statistics each week by students who achieve high distinction (HD) in the course is a normally distributed random variable with a mean of 7.5 hours and a standard deviation of 2.1 hours.
QUESTION TWENTY-ONE
What proportion of HD students study for more than 10 hours per week?
(a) Approximately 0.170
(b) approximately 0.117
(c) approximately -0.117
(d) approximately 0.270
(e) None of the above
QUESTION TWENTY-TWO
Find the probability that a HD student spends between 7 and 9 hours studying.
(a) approximately 0.36
(b) approximately 0.46
(c) approximately -0.46
(d) approximately -0.52
(e) None of the above
QUESTION TWENTY-THREE
What proportion of HD students spend less than three hours studying?
(a) -0.0162
(b) -0.9838
(c) 0.9838
(d) 0.0162
(e) None of the above
QUESTION TWENTY-FOUR
What is the amount of time below which only 5% of all HD students spend studying?
(a) approximately 4 hours
(b) approximately 2 hours
(c) approximately 1 hour and 30 minutes
(d) approximately 1 hour and 45 minutes
(e) None of the above
QUESTION TWENTY-FIVE
What is the best interpretation for this?
(a) The minimum hours studiedby the top 5% of students is approximately 4 hours
(b) The minimum hours studiedby the bottom 5% of students is approximately 4 hours
(c) The minimum hours studiedby the top 5% of students is approximately 2 hours
(d) The minimum hours studiedby the bottom 5% of students is approximately 2 hours
(e) The minimum hours studiedby the top 5% of students is approximately 1 hour and 30 minutes
REQUIRED: Answer questions 26 - 30 based on the following information
The following table lists the average price and quantity consumed for a selection of food products.
QUESTION TWENTY-SIX
What is the unweighted aggregate price index in 2005 using 2000 as the base year?
(a) 106.02
(b) 67.59
(c) 147.95
(d) 335.02
(e) None of the above
QUESTION TWENTY-SEVEN
What is the best interpretation for this?
(a) The overall price rise from 2000 to 2005 was 6.02%
(b) The overall price rise from 2000 to 2005 was 67.59%
(c) The overall price rise from 2000 to 2005 was 47.95%
(d) The overall price rise from 2000 to 2005 was 235.02%
(e) None of the above
QUESTION TWENTY-EIGHT
What is the Paasche price index in 2005 using 2000 as the base year?
(a) approximately 163.12
(b) approximately 165.29
(c) approximately 147.95
(d) approximately 169.55
(e) None of the above
QUESTION TWENTY-NINE
What is the Paasche price index in 2010 using 2000 as the base year?
(a) 309.92
(b) 335.02
(c) 343.34
(d) 323.15
(e) None of the above
QUESTION THIRTY
What is the best interpretation for this?
(a) The overall price rise from 2000 to 2010 was 223.15%
(b) The overall price rise from 2000 to 2010 was 243.34%
(c) The overall price rise from 2000 to 2010 was 209.92%
(d) The overall price rise from 2000 to 2010 was 235.02%
(e) None of the above
REQUIRED: Answer questions 31 - 38 based on the following information
In recent times many leading economists have commented that the world economy is about to enter a second global recession. Suppose you have been commissioned by the World Bank to survey the view of the various central bank heads. You conduct a survey of 20 central bank heads and find that 8 believe the world is heading for another recession
QUESTION THIRTY-ONE
What is the sample proportion?
(a) 0.6
(b) 0.4
(c) 8
(d) 0.1095
(e) None of the above
QUESTION THIRTY-TWO
What is the standard error?
(a) approximately 0.1095
(b) approximately 0.0120
(c) approximately 0.4000
(d) approximately 0.1118
(e) None of the above
QUESTION THIRTY-THREE
If you were to construct a 95% confidence interval, what critical value (s) would you use?
(a) 1.645
(b) 1.960
(c) 2.093
(d) 2.433
(e) None of the above
QUESTION THIRTY-FOUR
What is the 95% confidence interval for the proportion of central bank heads who think the world is heading for another recession?
(a) 0.1707 < π < 0.6293
(b) 0.1854 < π < 0.6146
(c) 0.1334 < π < 0.6666
(d) 0.2198 < π < 0.5802
(e) None of the above
QUESTION THIRTY-FIVE
What is the best interpretation of the confidence interval?
(a) We are 95% confident that the proportion of leading economists who believe the world is heading for another recession is between 18.54% and 61.46%
(b) We are 95% confident that the proportion of leading economists who believe the world is heading for another recession is between 17.07% and 62.93%
(c) We are 95% confident that the proportion of leading economists who believe the world is heading for another recession is between 13.34% and 66.66%
(d) We are 95% confident that the proportion of leading economists who believe the world is heading for another recession is between 21.98% and 58.02%
(e) None of the above
QUESTION THIRTY-SIX
If the population standard deviation (σ) is unknown, what is the most appropriate distribution to obtain critical values from?
(a) Student's t-distribution
(b) Z distribution
(c) Standard Normal distribution
(d) Uniform distribution
(e) None of the above
QUESTION THIRTY-SEVEN
If you were constructing a 99% confidence interval with σ known, what critical value would you use
(a) 1.645
(b) 1.280
(c) 1.960
(d) 2.58
(e) None of the above
QUESTION THIRTY-EIGHT
If you were constructing a 99% confidence interval with σ unknown, what critical value would you use?
(a) 1.280
(b) 1.960
(c) 2.576
(d) 1.645
(e) None of the above
REQUIRED: Answer questions 39 - 40 based on the following information
Suppose you conduct a follow up study regarding the number of economists who think the world is heading for another recession. You decide that the original survey of 20 economists was too small a sample size (leading to unacceptably high levels of error).
QUESTION THIRTY-NINE
You conduct another survey to estimate the population proportion but wish to be within ± 3% of the true proportion with 95% confidence. What sample size (n) is required? (Assume π = 0.4)
(a) 1024
(b) 1025
(c) 683
(d) 1024.39
(e) None of the above
QUESTION FORTY
When estimating the sample size in this way, you should always:
(a) Use 2 decimal places
(b) Round down
(c) Round up
(d) Round to the closest integer
(e) None of the above
REQUIRED: Answer questions 41 - 50 based on the following information
A real estate developer wanted to determine how much a good view adds to property prices in Victoria. A sample of property sales ($) data was collected, including land size (m2), age of the house (years), number of rooms and a variable where 1 equals a property with a good view and 0 equals a property not having a good view. A regression was estimated as follows:
QUESTION FORTY-ONE
What is the best interpretation for the estimated coefficient for age?
(a) For every additional year, the estimated property price does not change
(b) For every additional year, the estimated property price increases by $347.9
(c) For every additional year, the estimated property price increases by $64.72
(d) For every additional year, the estimated property price decreases by $347.9
(e) None of the above
QUESTION FORTY-TWO
What is the best interpretation for the estimated coefficient for rooms?
(a) For every additional room, the estimated property price decreases by $16409.5
(b) For every additional room, the estimated property price increases by $16409.5
(c) For every additional room, the estimated property price increases by $2562.04
(d) For every additional room, the estimated property price does not change
(e) None of the above
QUESTION FORTY-THREE
Does view have a statistically significant effect on property prices at the 5% level of significance? Why/Why not?
(a) Yes, as the p-value is less than 0.05
(b) No, because the t-stat is too low
(c) No, because the p-value is less than 1.96
(d) Not enough information
(e) None of the above
QUESTION FORTY-FOUR
Interpret the 95% confidence interval associated with the coefficient view:
(a) Irrelevant as the view does not have a significant effect on property price
(b) We are 95% confident that a good view will increase property price by $17386.98
(c) We are 95% confident that a good view will decrease property price between $4799.29 and $29974.68
(d) We are 95% confident that a good view will increase property price between $4799.29 and $29974.68
(e) None of the above
QUESTION FORTY-FIVE
Interpret the R2
(a) 31.81% of variation in property prices can be explained by variation in the X variables
(b) 56.4% of variation in property prices can be explained by variation in the Y variables
(c) 30.94% of variation in property prices can be explained by variation in the X variables
(d) 31.81% of variation in property prices can be explained by variation in the Y variables
(e) None of the above
QUESTION FORTY-SIX
In a multivariate model, is the R2 or adjusted R2 better? Why?
(a) There is no difference between the two as they merely measure different aspects of model performance
(b) R2 since it is unaffected by irrelevant variables
(c) Adjusted R2 since it penalizes the excessive use of insignificant regressors
(d) R2 since the standard error is small relative to the mean
(e) None of the above
QUESTION FORTY-SEVEN
What is the purpose of the F-test?
(a) To test the significance of the observations
(b) To test the average model fit
(c) To test the individual significance of the regressors
(d) To test the overall significance of the model
(e) None of the above
QUESTION FORTY-EIGHT
What is the null and alternative hypothesis in the F-test?
(a) H0: β1 = β2 = β3 = β4 < 0, H1: At least one βj ≥ 0
(b) H0: β1 < β2 < β3 < β4 < 0, H1: At least one βj ≥ 0
(c) H0: β1 = β2 = β3 = β4 = 0, H1: At least one βj ≠ 0
(d) H0: β1 ≠ β2 ≠ β3 ≠ β4 ≠ 0, H1: At least one βj = 0
(e) None of the above
QUESTION FORTY-NINE
What are the results of the F-test?
(a) Age, rooms and view are insignificant but land is statistically significant
(b) None of the variables has a significant effect on property prices
(c) At least one of the independent variables has a significant effect on property prices
(d) Not enough information
(e) None of the above
QUESTION FIFTY
Predict the price of a 40 year house with 6 rooms, which is on a property of 1000 m2 with a nice view
(a) approximately $64,466
(b) approximately $178, 246
(c) approximately $72,156
(d) approximately $78, 246
(e) None of the above