Question

Test the claim that the proportion of people who own cats is significantly different than 40% at the 0.1 significance level. The null and alternative hypothesis would be: OH:P < 0.4 Hp > 0.4 OH = 0.4 H +0.4 H:p = 0.4 Hp + 0.4 Ho:p = 0.4 HP < 0.4 Hou < 0.4 H:H > 0.4 H: > 0.4 HAM < 0.4 The test is: two-tailed right-tailed left-tailed

Answer 1

Solution:

This is a two tailed test,

Test statistics

z = ($\hat p$ - $p_{0}$ ) / $\sqrt{}$ $p_{0}$*(1-$p_{0}$) / n

= ( 0.36 - 0.40) / $\sqrt{}$ (0.40*0.60) / 800

= -2.31

P-value = 2 * P(Z < z )

= 2 * P( Z < -2.31 )

= 2 * 0.0104

= 0.0208

Therefore, P-value = 0.0208 < 0.1, Reject the null hypothesis.