Question

10% of Amazon packages are damaged. In an effort to lower this percentage, the new packaging material is introduced. To test whether the new packaging material is successful, a random sample of 300 packages is inspected and 24 are damaged. Testing at the significance level of a= 0.5.

Find:

a. H_0, H_a

b. p̂

c. Z- Value

d. P- Value

e. Conclusion (reject H₀ or do not reject H₀ )

Answer 1

Solution :

This is the two tailed test .

The null and alternative hypothesis is

H₀ : p = 0.10

H_a : p 0.10

= x / n = 24 / 300 = 0.08

P₀ = 0.10

1 - P₀ = 0.90

Test statistic = z

= - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.08 - 0.10 / [(0.10 * 0.90) / 300]

= -1.155

P(z < -1.155) = 0.124

P-value = 0.124

= 0.05

P-value >

Fail to reject the (H0).