Question

A random sample of 20 binomial trials resulted in 8 successes. Test the claim that the population proportion of successes does not equal 0.50. Use a level of significance of 0.05.

(c) Compute p̂.


Compute the corresponding standardized sample test statistic. (Round your answer to two decimal places.)


(d) Find the P-value of the test statistic. (Round your answer to four decimal places.)

Answer 1

Solution :

This is the two tailed test .

The null and alternative hypothesis is

H0 : p =0.50

Ha : p 0.50

n = 20

x =8

= x / n = 8 / 20 = 0.40

P0 = 0.50

1 - P0 = 1 -0.50 =0.50

Test statistic = z

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

=0.40 -0.50/ [0.50*0.50 / 20]

= −0.894

Test statistic = z =−0.89

P-value = 0.3711

= 0.05

P-value ≥  

0.3711 ≥ 0.05

Fail to reject the null hypothesis .

There is insufficient evidence to suggest that