To determine whether a single coin is fair, the coin was tossed 250 times, and heads was observed 140 times. The value of the test statistic is:
A) 140
B) 3.6
C) 110
D) 30
E) 20

Question

Quizplus · Accepted Answer

To determine whether a coin is fair, we can use a hypothesis test where the null hypothesis H0 is that the coin is fair, i.e. the probability of observing heads is 0.5, and the alternative hypothesis Ha is that the coin is not fair, i.e. the probability of observing heads is either greater or less than 0.5. 
We can use the normal approximation to the binomial distribution, since n=250 is large and p=0.5 is not too close to 0 or 1. 
The test statistic is given by 
z=(x-μ)/σ, where x is the number of heads observed, μ=np=125, and σ=sqrt(np(1-p))=7.91. 
Substituting x=140 into the formula we get 
z=(140-125)/7.91=1.89.
Therefore, the value of the test statistic is 1.89, which corresponds to choice B.

To Determine Whether a Single Coin Is Fair, the Coin