Question

According to one source, 50% of plane crashes are due at least in part to pilot error. Suppose that in a random sample of 100 separate airplane accidents, 59 of them were due to pilot error (at least in part.) Test the null hypothesis that the proportion of airplane accidents due to pilot error is not 0.50. Use a significance level of 0.05.

Answer 1

Solution :

Given that,

n = 100

x = 59

= x / n = 59/100 = 0.59

Hypothesis:

H0 : P 0.50

Ha : P   0.50

Test Statistic:

Z =   - P / ( ((P * (1 - P)) / n)

Z = 0.59 - 0.50/  ( ((0.50* 0.50) / 100)

Z = 1.8

Z = 1.8

P- value = 0.0719

P-value >0.05 , So Fail to reject H0.