Question

A state’s environmental agency worries that many semi-trailer trucks on highway may be violating clean air emission standards due to faulty emission control system. The agency checked a sample of vehicles by random sampling, and found 9 out of 60 with faulty emission control systems. We want to test if this result can be taken as an evidence that more than 10% of semis on highway have faulty emission control system, using significance level of 5%. Report p-value. (Use 3 decimals.)

Answer 1

Solution :

This is the right tailed test .

The null and alternative hypothesis is

H₀ : p = 0.10

H_a : p > 0.10

= x / n = 9 / 60 = 0.15

P₀ = 0.10

1 - P₀ = 0.90

Test statistic = z

= - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.15 - 0.10 / [(0.10 * 0.90) / 60]

= 1.29

P(z > 1.29) = 1 - P(z < 1.29) = 1 - 0.9015 = 0.0985

P-value = 0.0985 = 0.099