Question

An article published in the Washington Post claims that 45 percent of all Americans have brown eyes. A random sample of ?=84 college students found 31 who had brown eyes.

Consider testing ?0:?=.45 ??:?≠.45

(a) The test statistic is ? = -1.491

**** (b) P-value = ???

Answer 1

Solution :

This is the two tailed test .

The null and alternative hypothesis is

H0 : p = 0.45

Ha : p 0.45

n = 84

x = 31

= x / n = 31 / 84 = 0.369

P0 = 0.45

1 - P0 = 1 - 0.45 =0.55

a ) Test statistic = z

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

=0.369 -0.45 / [(0.45*0.55) / 84]

= −1.491

Test statistic = z =−1.49

b ) P value = 2 * 0.0681 =0.1362