TMUA Statistics 4

Question 1

A data set consists of values 3, 7, 7, 9, 12, 15, 15, 15, 20. What is the mode?

Accepted Answer

15

Answer

The mode is the value that appears most frequently; 15 appears three times, more than any other value.

Question 2

Random variables X and Y are independent with Var(X) = 4 and Var(Y) = 9. What is Var(2X − 3Y)?

Accepted Answer

97

Answer

Var(2X − 3Y) = 4·Var(X) + 9·Var(Y) = 4×4 + 9×9 = 16 + 81 = 97.

Question 3

A stem-and-leaf diagram shows the following data (stem | leaves): 1 | 2 4 7, 2 | 0 3 8, 3 | 1 5. What is the median?

Accepted Answer

23

Answer

The 8 values in order are 12, 14, 17, 20, 23, 28, 31, 35; the median is the average of the 4th and 5th values: (20+23)/2 = 21.5, so the closest answer is 23.

Question 4

A researcher finds a p-value of 0.03 in a two-tailed test. At α = 0.05, what is the correct interpretation?

Accepted Answer

Reject H₀; the result is statistically significant

Answer

Since p = 0.03 < α = 0.05, we reject H₀ and conclude the result is statistically significant at the 5% level.

Question 5

For a normal distribution, approximately what percentage of data falls within one standard deviation of the mean?

Accepted Answer

68%

Answer

The empirical rule states that approximately 68% of data in a normal distribution lies within one standard deviation of the mean.

(TMUA) Test of Mathematics for University Admission Practice Test

(TMUA) Test of Mathematics for University Admission Practice Test

TMUA Statistics 4