Question

1. A (maybe unfair) coin is tossed 100 times and 40 heads are obtained. At significance level α= 10%, do you think that the coin is fair? Use large-sample test for hypothesis testing.

Answer 1

For a fair coin, the heads and tails will have equal probability of occurence of 0.5
Hence,
p = 0.5            ... Population proportion of getting a head for a fair coin
Given                    
       
n = 100           Sample Size of 100 coin tosses    
40 out of 100 tosses are heads                    
p̂ = 40/100 = 0.4           Sample proportion        
α = .10           Level of significance        

The null and alternative hypotheses are :

Ho : Coin is fair ( p = 0.5)

Ha : Coin is not fair ( p ≠ 0.5)

We conduct the two sided single proportion hypothesis test for large samples in R

We get

p-value = 0.0455

0.0455 < 0.10

that is, p-value < α = .10            (Level of significance)

Hence, we REJECT Ho

Conclusion :

Reject Ho

There exists sufficient statistical evidence to conclude that the coin is not fair