To determine whether a single coin is fair,the coin was tossed 100 times,and the head was observed 60 times.The value of the test statistic is:
A)0.40
B)1.05
C)0.6
D)1.9

Question

Quizplus · Accepted Answer

The test statistic for a test of proportion is given by:

z = (p - P) / sqrt(P(1-P)/n)

where,
p = sample proportion 
P = hypothesized population proportion 
n = sample size

Here, the null hypothesis is that the coin is fair, i.e. P = 0.5
The alternative hypothesis is that the coin is not fair, i.e. P ≠ 0.5

The sample proportion is p = 60/100 = 0.6

Plugging these values into the formula, we get:

z = (0.6 - 0.5) / sqrt(0.5(1-0.5)/100) = 1.897

Therefore, the test statistic is 1.897, which is closest to option D, 1.9.

To Determine Whether a Single Coin Is Fair,the Coin Was