Question

A new drug has been developed to treat a particular condition, and it is alleged to be more effective than traditional treatment. An experiment will be conducted to test whether the statement is true. To perform a hypothesis test, a confidence level of 99% is selected for the hypothesis test. The new drug was administered to a sample of 200 individuals with the condition, selected at random, another 300 individuals were selected to whom the traditional treatment was administered. Of the 200 individuals treated with the new drug, 120 were completely cured. Of those treated with the traditional method, 220 were completely cured.

1. Is there statistical evidence to support the claim that the new drug is more effective? Take the proper test and finish

2. If you were a patient of this condition, which treatment would you select? justify

Answer 1

P1=proportion of sample which cured by new drug

P2=proportion of sample which cured by traditional method

For sample 1, we have that the sample size is N1 ​=200, the number of favorable cases isX1​=120, so then the sample proportion is X1/N1=0.6

For sample 2, we have that the sample size is N2​=300, the number of favorable cases is X2​=220, so then the sample proportion is X2/N2=0.7333

The value of the pooled proportion is computed as (X1+X2)/(N1+N2)=0.68

Also, the given significance level is α=0.01.

(1) Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

Ho:p1​=p2​

H1:p1​>p2​

This corresponds to a right-tailed test, for which a z-test for two population proportions needs to be conducted.

(2) Rejection Region

Based on the information provided, the significance level is α=0.01, and the critical value for a right-tailed test is zc​=2.33.

The rejection region for this right-tailed test is R={z:z>2.33}

(3) Test Statistics

The z-statistic is computed as follows:

Z=0.6-0.73330.68*1-0.68*1200-(1300) =−3.131

(4) Decision about the null hypothesis

Since it is observed that z=−3.131≤zc​=2.33, it is then concluded that the null hypothesis is not rejected.

Using the P-value approach: The p-value is p=0.9991, and since p=0.9991≥0.01, it is concluded that the null hypothesis is not rejected.

(5) Conclusion

It is concluded that the null hypothesis Ho is not rejected. Therefore, there is not enough evidence to claim that the effect of new drug ​ is more than effect by traditional method​, at the 0.01 significance level.

2. If I were a patient I select traditional method since it is as effictive as new drug.