Question

A factory that puts together car parts is known to produce 3% defective cars. Following a fire outbreak at the factory, reconstruction is carried out which may result in a change in the percentage of defective cars produced. To investigate this possibility, a random sample of 200 cars is taken from the production and a count reveals 14 defective cars. What may be concluded? Run a significance test using a 0.05 α-level of significance.

Answer 1

Solution:

p = 3% = 0.03

Claim : p is changed i,e p 0.03

The null and alternative hypothesis are

H₀ : p = 0.03 vs H_a : p 0.03

n = 200

x = 14

Let   be the sample proportion.

= x/n = 14/200= 0.07

The test statistic z is

z =   

=  (0.07 - 0.3)/[0.03*(1 - 0.03)/200]

= 3.32

3) p value

sign in H1 indicates that the test id "Two Tailed"

p value = 2 * P(Z < -3.32)

= 2 * 0.0005

= 0.0010

p value = 0.0010 is less than = 0.05

Reject H0 . There is sufficient evidence to conclude that a change in the percentage of defective cars produced.