Question

In a clinical study of an allergy drug, 109 of the 202 subjects reported experiencing significant relief from their symptoms. at the .01 significance level, test the claim that more than 50% of those using the drug experienced relief. what is the final conclusion in simple nontechnical terms?

Answer 1

Solution :

Given that,

= 0.50

1 - = 0.50

n = 202

x = 109

Level of significance = = 0.01

Point estimate = sample proportion = = x / n = 0.540

This a right (One) tailed test.

The null and alternative hypothesis is,

Ho: p = 0.50

Ha: p 0.50

Test statistics

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

= ( 0.540 - 0.50) / (0.50*0.50) /202

= 1.126

Critical value of  the significance level is α = 0.01, and the critical value for a right-tailed test is

= 2.33

Since it is observed that ,z = 1.126 < = 2.33, it is then concluded that the null hypothesis is fails to rejected.

P-value = P( Z > z)

= 1 - P(Z <z )

= 1- P(Z < 1.126)

= 0.1301

The p-value is p = 0.1301, and since p = 0.1301 > 0.01, it is concluded that the null hypothesis is fails to rejected.

Conclusion:

It is concluded that the null hypothesis Ho is fails to rejected. Therefore, there is not enough evidence to claim that that more than 50% of those using the drug experienced relief at the α = 0.01 significance level.