Question

Consider the following hypothesis test:

H₀: p .8
H_a: p > .8

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

16. Determine the standard error of the proportion.

17. Compute the value of the test statistic.

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

Answer 1

Solution :

This is one tailed test .

The null and alternative hypothesis is

H0 : p = 0.8

Ha : p > 0.8

= 0.853

1 - = 1 - 0.853 = 0.147

1 - P0 = 1 - 0.8 = 0.2

16)

Standard Error = [ * (1 - ) / n]

= [0.853 * 0.147) / 500]

= 0.02

17)

Test statistic = z

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

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

= 2.96

18)

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

P-value = 0.0015

= 0.05

P-value <

Reject the null hypothesis .