statistic and probability

Question

A tube light producer company claims that 80% of the tube lights manufactured by it

have life time more than 2 years. The consumer forum thinks that the percentage is

less. The survey conducted by the consumer forum to challenge the company’s claim

indicates that out of 150 randomly selected tube lights, 110 had life time more than 2

years. Does this evidence lead to the rejection of the null hypothesis at 5% level of

significance?

Answer 1

Ho: p = 0.8

Ha: p < 0.8

n = 150

phat 110/150 = 0.73

z = (phat - p)/sqrt(p * (1-p)/n)

z = (0.73 - 0.8)/sqrt(0.8 * 0.2/150) = -2.14

critical value for left-sided test at 0.05 level of significance = -1.96

since computed z < critical value, reject Ho.