Question

A random sample of n = 1400 observations from a binomial population produced x = 388. H0: p = 0.3 versus Ha: p ? 0.3 (b) Calculate the test statistic and its p-value. (Round your test statistic to two decimal places and your p-value to four decimal places.) z = p-value =

Answer 1

H0: p = 0.3

Ha: p 0.3

H0: p = 0.3 ha: p notequalto 0.3 Sample proportion p^- = 388/1400 = 0.277 Test statistics z = p^- - p/sqrt(p(1-p)/n) = 0.277 - 0.30/sqrt(0.30 * 0.70/1400) = -1.88 This is test statistics value. Two tailed p-value calculated as p-value = 2 * P(Z < -1.88) (2 is multiplied to probability since this is two tailed test) = 2 * 0.0301 = 0.0602

Sample proportion $\hat{p}$ = 388 / 1400 = 0.277

Test statistics

Z = $\hat{p}$ - p / sqrt( p( 1 -p ) / n)

= 0.277 - 0.30 / sqrt( 0.30 * 0.70 / 1400)

= -1.88

This is test statistics value.

Two tailed p-value calculated as

p-value = 2 * P( Z < -1.88) ( 2 is multiplied to probability since this is two tailed test)

= 2 * 0.0301

= 0.0602