Question

In a random sample of 300 patients, 21 experience nausea. A drug manufacturer claims that fewer than 10% of patients who take its new drug for treating Alzheimer's disease will experience nausea. Calculate the P-value. Round your answer to 3 decimal places.

In a random sample of 300 patients, 21 experience nausea. A drug manufacturer claims that fewer than 10% of patients who take its new drug for treating Alzheimer's disease will experience nausea. Based on your P-value in the previous question, will we reject or fail to reject the null hypothesis?

Answer 1

Solution :

Given that,

n = 300

x = 21

Point estimate = sample proportion = = x / n = 21/300 = 0.07

= 10% = 0.10

1 - = 1 - 0.10 = 0.90

= 0.05

a)

This is a left (One) tailed test,

Ho: P = 0.10

Ha: P < 0.10

#

The test statistics

z = ( - )/( *( 1- ) )/n

= ( 0.07 - 0.10)/( 0.10*0.90)/300

= -1.73

p-value = P(Z < z )

= P( Z <-1.73)

value of z is obtain from standard normal table

= 0.0416

#P-value:0.0416

Ansb:

#value is p = 0.0416< = 0.05, it is concluded that the null hypothesis is rejected

#we reject the null hypothesis.