Question

Suppose that 500 parts are inspected for quality and 15 are rejected.

(a) Test the hypothesis H₀: p = 0.02 against H₁: p > 0.02 at α = 0.05.

(b) Find the p-value.

Answer 1

Solution :

This is the right tailed test .

The null and alternative hypothesis is

H0 : p = 0.02

Ha : p > 0.02

= x / n = 15 /500 = 0.03

P0 = 0.02

1 - P0 = 1 -0.02 = 0.98

Test statistic = z

= - P0 / [P0 * (1 - P0 ) / n]

=0.03 -0.02 / [0.02*(0.98) /500 ]

= 1.597

P(z > 1.597) = 1 - P(z < 1.597 ) = 0.0551

P-value = 0.0551

= 0.02

0.0551 < 0.02

Do not reject the null hypothesis .

There is insufficient evidence to suggest that