Question

Suppose you are testing H0:p=0.45, H1:p>0.45. A random sample of 310 people produces a value of p ̂=0.465. Use α=0.05 to test this hypotheses

Answer 1

The following hypotheses are being tested

$H_0:p=0.45$

$H_1:p>0.45$

$Z=\frac {p-p_0}{\sqrt{\frac{p_0(1-p_0)}{n}}}$

$=\frac{0.465-0.45}{\sqrt{\frac{0.45(1-0.45)}{310}}}$

=0.5309

The z critical valued is 1.96.

Since 0.5309 is less than 1.96 the null hypothesis is not rejected.

P=0.45.