TMUA Data Analysis & Statistical Interpretation 5

Question 1

A random variable X has E(X) = 5 and Var(X) = 4. What are E(2X + 3) and Var(2X + 3)?

Accepted Answer

E = 13, Var = 16

Answer

E = 13, Var = 11

Answer

E = 10, Var = 8

Answer

E = 13, Var = 8

Question 2

A two-way table shows: P(A) = 0.6, P(B|A) = 0.5, P(B|A') = 0.2. What is P(B)?

Accepted Answer

0.38

Answer

0.30

Answer

0.70

Answer

0.50

Question 3

Data values are 5, 10, 15, 20, 25. Which transformation would most linearise the relationship if the original data appears exponential?

Accepted Answer

Taking the logarithm of each value

Answer

Squaring each value

Answer

Taking the square root of each value

Answer

Multiplying each value by a constant

Question 4

A bag contains 4 red and 6 blue balls. Two balls are drawn without replacement. What is the probability that both are red?

Accepted Answer

2/15

Answer

4/25

Answer

1/6

Answer

2/25

Question 5

A data analyst calculates Spearman's rank correlation coefficient for two variables and obtains rs = −0.85. What does this indicate?

Accepted Answer

A strong negative monotonic relationship

Answer

A strong positive linear relationship

Answer

No relationship between the variables

Answer

A weak negative linear relationship

Question 6

A time series shows an upward trend with seasonal variation. Which method is most appropriate to isolate the trend?

Accepted Answer

Computing a moving average

Answer

Calculating the mode

Answer

Plotting a scatter graph

Answer

Finding the interquartile range

Question 7

A sample of size n = 100 has a mean of 42 and standard deviation of 8. Using the Central Limit Theorem, what is the standard error of the mean?

Accepted Answer

0.8

Answer

8

Answer

0.64

Answer

4