# Statistics Questions

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Question 6
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The height of your workstation desk is one of the essential criteria for creating the perfect ergonomic workspace, whether at home
or in your office. A company’s plant manager is currently considering two designs of ergonomic computer desks for their
employees. An experiment is performed to help with the purchasing decision. 50 randomly selected employees used the design A
computer desk, and another 50 employees used the design B computer desk. On a 15-point scale, their comfort level was
recorded in the EXCEL file ErgonomicDeskDesign.xlsx. Use EXCEL and an appropriate hypothesis test to help the plant manager to
Research Question: Are the comfort levels of the two designs (design A and design B) different?
Answer the following questions by choosing the most correct option or typing the answer:
1. (1 mark) The most appropriate test for these data is:
2. (1 mark) Which graphical display would be useful to check normality assumption for this hypothesis?
A. Figure 1
B. Figure 2
C. Figure 3
D. Figure 4
E. Figure 1 & 2
F. Figure 3 & 4
G. No need to check normality assumption
H. All four figures are needed
3. (1 mark) How can you check the assumption of equal variances?
A. Comparative boxplots could be used (e.g. if the sizes of boxes are similar or not)
B. Descriptive statistics such as variance, standard deviation and range could be used
C. Descriptive statistics such as mean and median could be used
D. The histogram of differences could be used
E. Both A & B could be used
F. No need to check the assumption of equal variances
For the remaining questions you may assume that any relevant assumptions have been met.
4. (2 marks) The absolute value of the test statistic is equal to
(3dp)
5. (1 mark) The degrees of freedom is equal to
(Integer)
6. (1 mark) The p-value is larger than 0.05
7. (2 marks) The test shows that the comfort level ratings were
A. significantly different between design A and design B, possibly greater for design A.
B. significantly different between design A and design B, possibly greater for design B.
C. not significantly different between the two design of the computer desks.
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Question 5
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With inflation and the impact of higher prices on households’ cost of living under the spotlight, the Office for National
Statistics(ONS) announced changes to the 2022 basket of goods to reflect people’s inflation experiences in the UK, in line with the
current circumstances.
Below are three regression outputs fitting the consumer prices index (CPI) to a different basket of goods, each basket of goods
consists of 60 consumer items.
Coefficients
Standard Error
t Stat
P-value
Intercept
3.130
0.498
6.284
0
0.289
0.049
5.839
0
Coefficients
Standard Error
t Stat
P-value
Intercept
3.567
0.184
19.396
0
0.196
0.015
13.456
0
Coefficients
Standard Error
t Stat
P-value
Intercept
5.408
0.213
25.393
0.000
0.054
0.019
2.836
0.006
Regression Statistics
Multiple R
**
0.87
0.349
R square
0.37
0.757
0.122
0.359
0.753
0.107
Standard Error
0.411
0.287
0.426
Observations
60
60
60
Assume that assumptions for simple linear regression are satisfied. Use the above tables to answer the following questions, either
choose the most correct option, or type in the answer to the number of decimal places specified.
1. (1 mark) The correlation between CPI and Basket of Goods 1 is:
(3dp – remember to include a negative sign if appropriate)
The economists are interested in which basket of goods most accurately predicts CPI. Use the regression results to answer
the following questions.
2. (1 marks) Which variable is a better predictor of CPI?
D: None of them is a good predictor of CPI.
3. (2 marks) Why? Choose the most appropriate answers to justify your answer to Question 2 above.
A. Correlation between CPI and Basket of Goods 1 is the highest.
B. Correlation between CPI and Basket of Goods 2 is the highest.
C. Correlation between CPI and Basket of Goods 3 is the highest.
D. The slope of regression equation for the linear relationship between CPI and Basket of Goods 1 was significantly different
than zero.
E. The slope of regression equation for the linear relationship between CPI and Basket of Goods 2 was significantly different
than zero.
F. The slope of regression equation for the linear relationship between CPI and Basket of Goods 3 was significantly different
than zero.
G. Both A & D
H. Both B & E
I. Both C & F
J. There is not enough information to make a decision.
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Question 4
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COVID-19 deaths are underreported in different countries for different reasons, including limited capacity to test for infection,
inadequate death registration systems, and inaccurate reporting due to political factors. As a result, health officials based their
analysis on the concept of “excess mortality”– a measure of the difference between deaths from all causes observed or estimated
during the pandemic and the number of deaths that would be expected from the past mortality trends. For example, the
Economist, estimates 22.05 million (95% uncertainty interval 21.48-22.62 million) excess deaths between 1 January 2020 and 31
December 2021.
The Excel file ExcessDeaths.xlsx contains excess deaths estimates (in millions) for the same period, from 38 randomly selected from
health experts/institutions worldwide. Use EXCEL and an appropriate hypothesis test to answer the following research question,
assuming assumptions are satisfied.
Research Question: Could the mean excess deaths due to the COVID-19 pandemic equal 22.05 million between 1 January
2020 and 31 December 2021, as estimated by the Economist?
1. (1 mark) What is the sample mean?
million (3dp)
2. (1 mark) What is the sample standard deviation?
million (3dp)
3. (1 mark) The most appropriate hypothesis test for these data is
4. (1 mark) The null hypothesis is that the mean estimated excess deaths from COVID-19 equal
(Hint: this is
the value of μ0 in the H0 : μ = μ0 )
5. (2 mark) What is the absolute value of the test statistic ?
(3dp)
6. (2 mark) Is the p-value for this test statistic greater or less than 0.05?
7. (3 mark) Calculate a 95% confidence interval to estimate the mean excess deaths due to the COVID-19 between 1 January
2020 and 31 December 2021.
The Absolute Value of the Critical Value for a 95% confidence interval is
(3dp)
Lower Bound =
million (3dp)
Upper Bound =
million (3dp)
8. (1 mark) What is the most appropriate conclusion for this test?
A. The excess deaths are significantly different than the hypothesised value, possibly greater.
B. The excess deaths are significantly different than the hypothesised value, possibly lower.
C. The excess deaths could be the same as the hypothesised value.
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Question 2
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A growing body of studies challenges conventional assumptions that genetics or cultural differences lead some students – such as
indigenous or girls – to do poorly on standardised academic tests and other academic performances. To examine the phenomenon
associated with “stereotype threat”, researchers gave 47 randomly selected indigenous students a standardised test, asking
students to indicate their ethnicity before taking the test (First Week). In the second week, students were given the same test but
this time without revealing their race (Second Week). On a 100-point scale, students’ test scores were recorded in the EXCEL file
StandardisedTests.xlsx. Use EXCEL and an appropriate hypothesis test to help researchers to answer the following research
question.
Research Question: Was a negative stereotype activated simply by calling attention to one’s race that might impact
students’ test performance?
Answer the following questions by choosing the most correct option or typing the answer:
1. (1 mark) The most appropriate test for these data is:
2. (1 mark) Which graphical display would be useful to check normality assumption for this hypothesis?
A. Figure 1
B. Figure 2
C. Figure 3
D. Figure 4
E. Figure 1 & 2
F. Figure 3 & 4
G. No need to check normality assumption
H. All four figures are needed
3. (1 mark) How can you check the assumption of equal variances?
A. Comparative boxplots could be used (e.g. if the sizes of boxes are similar or not)
B. Descriptive statistics such as variance, standard deviation and range could be used
C. Descriptive statistics such as mean and median could be used
D. The histogram of differences could be used
E. Both A & B could be used
F. No need to check the assumption of equal variances
For the remaining questions you may assume that any relevant assumptions have been met.
4. (2 marks) The absolute value of the test statistic is equal to
(3dp)
5. (1 mark) The degrees of freedom is equal to
(Integer)
6. (1 mark) The p-value is larger than 0.05
7. (2 marks) The test shows that the test scores were
A. significantly different between the First Week and the Second Week, possibly higher in the First Week.
B. significantly different between the First Week and the Second Week, possibly higher for the Second Week.
C. not significantly different between the two weeks.
Copyright © Macquarie University. Copying or distribution of part or all of the contents in any form is prohibited.
Question 1
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With inflation and the impact of higher prices on households’ cost of living under the spotlight, the Office for National
Statistics(ONS) announced changes to the 2022 basket of goods to reflect people’s inflation experiences in the UK, in line with the
current circumstances.
Below are three regression outputs fitting the consumer prices index (CPI) to a different basket of goods, each basket of goods
consists of 42 consumer items.
Regression Statistics
Multiple R
0.327
0.782
0.427
R square
0.107
0.611
0.182
0.085
0.602
0.162
Standard Error
0.431
0.324
0.498
Observations
42
42
42
Intercept
Coefficients
Standard Error
t Stat
P-value
5.37
0.406
13.225
0
**
0.036
2.191
0.034
Coefficients
Standard Error
t Stat
P-value
Intercept
4.519
0.201
22.483
0
0.14
0.018
**
0
Coefficients
Standard Error
t Stat
P-value
Intercept
3.373
0.87
3.875
0
0.215
0.072
2.985
**
Assume that assumptions for simple linear regression are satisfied. Use the above tables to answer the following questions, either
choose the most correct option, or type in the answer to the number of decimal places specified.
1. (2 mark) What is the value of the regression slope between CPI and Basket of Goods 1?
(3dp – remember to include a negative sign if appropriate) with the degrees of freedom equals to
(integer)
2. (1 mark) What is the absolute value of the test statistic for CPI and Basket of Goods 2?
(3dp)
3. (2 mark) Is there a significant linear relationship between CPI and Basket of Goods 3
The economists are interested in which basket of goods most accurately predicts CPI. Use the regression results to answer
the following questions.
4. (1 marks) Which variable is a better predictor of CPI?
D: None of them is a good predictor of CPI.
5. (2 marks) Why? Choose the most appropriate answers to justify your answer to Question 4 above.
A. Correlation between CPI and Basket of Goods 1 is the highest.
B. Correlation between CPI and Basket of Goods 2 is the highest.
C. Correlation between CPI and Basket of Goods 3 is the highest.
D. The slope of regression equation for the linear relationship between CPI and Basket of Goods 1 was significantly different
than zero.
E. The slope of regression equation for the linear relationship between CPI and Basket of Goods 2 was significantly different
than zero.
F. The slope of regression equation for the linear relationship between CPI and Basket of Goods 3 was significantly different
than zero.
G. Both A & D
H. Both B & E
I. Both C & F
J. There is not enough information to make a decision.
Copyright © Macquarie University. Copying or distribution of part or all of the contents in any form is prohibited.