Question

A marketing company claims that it receives more than 6.5% responses from its Mailing. A sample of 600 mails yesterday revealed 50 responses. At the 0.10 level of significance, can we conclude that the claim is true? *

Answer 1

Solution:

1)

The null and alternative hypothesis are

H₀ : p = 0.065 vs H_a : p > 0.065

2)

n = 600

x = 50

Let   be the sample proportion.

= x/n = 50/600 = 0.0833

The test statistic z is

z =   

=  (0.0833 - 0.065)/[0.065*(1 - 0.065)/600]

= 1.82

Test Statistic z = 1.82

3)

> sign in Ha indicates that the test is "RIGHT TAILED"

For right tailed z test ,

p value = P(Z > z) = P(Z > 1.82) = 1 - P(Z < 1.82) = 1 - 0.9656 = 0.0344

p value = 0.0344

4)

Decision :

p value is less than given significance level α = 0.10

Reject the null hypothesis H₀

5)

Conclusion:

Yes , there is sufficient evidence to support the claim that more that 6.5% responses from its Mailing.