1) A researcher wanted to find the correlation between heights of father-and-son pairs. After collecting and analyzing his data, he realized that the device he had been using to measure height suffered from significant systematic bias causing every measurement to be too high by 10cm. He then corrected the values of all his analyses. After the correction, which values of the new data are expected to change significantly?
The standard deviation of son’s height and father’s height.
All the values in the other three options are expected to change significantly.
The average son’s height and average father’s height.
The correlation coefficient between heights of father-and-son pairs.
ANS : The average son’s height and average father’s height.
Pretty obvious that the standard deviation and correlation coefficient will not be touched given that every value differs by 10cm, and hence only the average values will change by 10cm
2) Tom tossed a coin into the air 7 times to test whether the coin is biased. The observed outcome was HHHTHHH. Consider the following statements:
I. Our opinion about the null hypothesis is the same if the outcome was THHHHHH.
II. We do not reject at the 5% significance level that the coin is unbiased.
Which of the statement(s) is/are true?
I and II
None of the statements are correct
I only
II only
ANS: I and II.
I) Null hypothesis is same given THHHHHH and HHHTHHH has the same probability
II) True
3) In a large department, it was discovered that, out of 64 people who have disease X, 48 had eaten tuna casserole from the canteen. Further investigation found that the same department also has 60 people who do not have disease X, although 20 of those had eaten tuna casserole from the canteen. What is the odds ratio of having disease X (for those who have eaten tuna casserole, relative to those who have not eaten)?
1/6
2/3
6
3/2
ANS: 6
Odds Ratio = (Disease ∩ Exposed) * (No Disease ∩ Unexposed) /
(Disease ∩ Unexposed) * (No Disease ∩ Exposed)
Odds Ratio = (48 * (60 - 20)) / ((64 - 48) * 20) = 6
4) The transcutaneous bilirubinometer is a new device that relies on flashes of light to calculate a baby’s bilirubin level. In a sample of baby girls, the correlation coefficient between bilirubin level from transcutaneous bilirubinometer and the traditional heel prick test is 0.99. In a sample of baby boys, the correlation coefficient is also 0.99. If we combine the two samples together and calculate the correlation, what would the correlation coefficient be in the combined sample?
Cannot be determined
0.99
Less than 0.99
More than 0.99
ANS : Cannot be determined
Use: https://www.socscistatistics.com/tests/pearson/default2.aspx
5) By "elderly", we mean a person who is more than 65 years old. In Singapore, the percentage of elderlies among women is higher than the percentage of elderlies among men. Consider the following statements:
I. In Singapore, the percentage of women among elderlies is higher than the percentage of women among the non-elderlies.
II. In Singapore, the percentage of women is higher than the percentage of men among elderlies.
Which of the statement(s) is/are true?
I only
II only
I and II
None of the statements are correct.
ANS: I is correct.
Prove by CounterExample:
Let E denote the Event of Elderly and W denote the Event of Women
(E ∩ W) = 11 and (E' ∩ W) = 9
(E ∩ W') = 50 and (E' ∩ W') = 50
Total Elderly = 61
Total Youth = 69
Total Male = 100
Total Female = 20
Total Population = 120
P(W | E) = 11/61 and P(W' | E) = 50/61 and P(W | E) < P(W' | E) which contrdicts (II)
P(W | E) = 11/61 and P(W | E') = 9 /59 and P(W | E) > P(W | E') which agrees with (I)
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