Question

A random sample of 100 people is selected, of whom 77 are right-handed. We concern about whether the proportion of people who are right-handed is different from 80%. Use these sample data to test the claim at significance level 0.05. Write out the full procedure that we went over in class.

Answer 1

Solution :

Given that,

n = 100

x = 77

= x / n = 77/100 = 0.77

Hypothesis:

H0 : P 0.80

Ha : P   0.80

Test Statistic:

Z =   - P / ( ((P * (1 - P)) / n)

Z = 0.77 - 0.80/  ( ((0.80* 0.20) / 100)

Z = -0.75

Z = -0.75

P- value = 0.4533

If P-value < 0.05 , then reject the null hupothesis.

P-value >0.05 Fail to reject H0 .

There is not suffcient evidence to support the claim.