Question

For A - C State whether the difference between what occurred and what you would have expected by chance is statistically significant. Discuss any implications of the statistical significance:

A. In 10 rolls of a six-sided die, the outcome of 6 never occurs.

B. A commuter enters a New York City subway car near Times Square and finds that it is occupied by 50 men, all of whom are bald.

C. In a clinical trial of a new drug intended to treat allergies, 5 of the 80 subjects in the treatment group experienced headaches and 8 of the 160 subjects in the control group experienced headaches.

Please explain with detail.

Answer 1

(A)

When a die is rolled, the probability of getting a 6 is 1/6. So in 10 rolls, the expected number of 6s will be 10 * (1/6) = 1.67 which is quite low. So we can say that not getting a 6 in 10 rolls can happen by pure chance. So the event is not statistically significant.

(B)

First, the chance of finding all 50 men in a car is low, and over that the probability of finding all 50 bald is even lower. So, this is an event which can't occur by chance alone. The result is statistically significant.

(C)

In this case, the difference between the two proportions is not significant at any level of significance. So, we can say that 5 of the 80 subjects in the treatment group experiencing headaches is something which could have happened by chance. It is not statistically significant.