Question

3. A marketing company claims 6 points 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? Your answer

Answer 1

Given,

p= 50 600 = 0.0833

The hypothesis is,

$\small H_0:p = 0.065$

$\small H_1:p > 0.065$

a = 0.10

we now that,

$\small Z = \frac{p - p_{0}} {\sqrt{\frac {p_{0}(1 - p_{0})} {n}}}$

$\small Z = \frac{0.0833 - 0.065} {\sqrt{\frac {0.065(1 - 0.065)} {600}}}$

$\small Z =1.82$

The corresponding p value is 0.03

At 0.10 level of significance we reject the null hypothesis since the p value is lesser than the significance level. Therefore we conclude that the company receives more than 0.065 response by its mail