Question

Consider the following hypothesis test:

H₀: p  .8
H_a: p > .8

A sample of 500 provided a sample proportion of .853.

i. Determine the standard error of the proportion.

ii. Compute the value of the test statistic.

iii. Determine the p-value; and at a 5% level, test the above hypotheses.

Answer 1

Solution :

This is the RIGHT tailed test .

The null and alternative hypothesis is

H0 : p = 0.8

Ha : p > 0.8

= 0.853

1 - P0 = 1-0.8=0.2

Test statistic = z

= - P0 / [P0 * (1 - P0 ) / n]

= 0.853-0.8/ [(0.8*0.2) /500 ]

= 0.017888

P(z >2.96 ) = 1 - P(z < 2.96) = 1-0.9985=0.0015

P-value = 0.0015

= 0.05

P-value <

Reject the null hypothesis .