Question

1. Below there is information for a 1 sample proportion hypothesis test:

H0:P= 0.75

HA:P> 0.75

α=0.01

1. What is the smallest value of the test statistic that would provide enough evidence to reject the null hypothesis? [3]

2. If the sample size is 50, what is the value of σp? [3]

3. If the test statistic is 2 (sample size is still 50), what is the value of p? [3]

Answer 1

Solution :

a ) This is the right two tailed test .

The null and alternative hypothesis is

H0 : p = 0.75

Ha : p >0.75

Test statistic = z = 2

P(z > 2 ) = 1 - P(z < 2 ) = 1 -0.9772

P-value = 0.0228

= 0.01

P-value >

0.0228 > 0.01

Fail to reject the null hypothesis .

There is insufficient evidence to suggest that  

b ) n = 50

P0 = 0.75

1 - P0 = 1 - 0.75 =0.25

= ( 1 - ) / n

=   0.75 * 0.25 / 50

= 0.0612

= 0.0612