Question

Test the hypothesis using the p-value approach

Upper H 0H0​: pequals=0.3

versus

Upper H 1H1​: pgreater than>0.3

n=200​; x=65, alphaαequals=0.01

Is np 0 left parenthesis 1 minus p 0 right parenthesisnp01−p0greater than or equals≥​10? yes or no

p value (round to three decimal places)=

(reject or do not reject?) the null hypothesis because the p value is (greater or less) than x.

Answer 1

Here we have n = 200, x = 65, so

The hypothesis are

H0: P = 0.3 v/s H1 : P > 0.3

Here np = 200 * 0.33 = 66 , nq = 200 * 0.67 = 134

Here both np and nq both are greater than or equal to 10.

The test statistic is

= 0.93

Here test is right tailed. So the p value is given by

p ( z > 0.93 ) = 1 - p ( z 0.93 )

Look in to te probability section of stnadard normal probability table for z value 0.9 and 0.03 . We get probability as 0.8238.

p ( z > 0.93 ) = 1 - 0.8238 = 0.176

Here p value > (0.01 ) . Hence we failed to reject null hypothesis.