Question

Suppose that a random sample of 100 observations from a population gives a value \hat{p} p ^ =.68 and you wish to test the null hypothesis that p = .75 against the alternate hypothesis that p<.75 Find the p-value for the test correct to 3 decimal places.

Answer 1

Solution :

This is the left tailed test .

The null and alternative hypothesis is

H0 : p =0.75

Ha : p <0.75

= 0.68

P0 = 0.75

1 - P0 = 1-0.75=0.25

Test statistic = z

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

=0.68-0.75 / [(0.75*0.25) / 100]

Z= -1.62

P(z <-1.62 ) = 0.0526 ( using z table )

P-value = 0.053