Question

In: Math

Suppose that a pharmaceutical company makes the assertion that Drug A has a stronger effect than...

Suppose that a pharmaceutical company makes the assertion that Drug A has a stronger effect than Drug B. To test this claim, 1000 randomly selected people were given the two drugs during different treatment periods. Among them, 600 preferred taking Drug A because of the stronger effect they felt; whereas 400 preferred Drug B. Determine whether there is sufficient evidence, at the 5% level of significance, to support the company’s claim that Drug A is stronger and preferred by more than 50% of patients.

Select one:

a. Reject H0; Drug A is stronger and preferred by less than 50% of patients.

b. Reject H0; Drug A is stronger and preferred by more than 50% of patients.

c. Do not reject H0; Drug A is stronger and preferred by less than 50% of patients.

d. Do not reject H0; Drug A is stronger and preferred by more than 50% of patients.

Solutions

Expert Solution

Solution:

Claim: a pharmaceutical company makes the assertion that Drug A has a stronger effect than Drug B and preferred by more than 50% of patients.

To test this claim, 1000 randomly selected people were given the two drugs during different treatment periods. Among them, 600 preferred taking Drug A because of the stronger effect they felt; whereas 400 preferred Drug B.

Let p = population proportion of people taking drug A = 50% = 0.50

and Sample proportion of people taking drug A =

Level of Significance = 0.05

Use following Steps:

Step 1) State H0 and H1:

H0: p = 0.50        Vs H1: p > 0.50

Step 2) Find z test statistic value:

Step 3) Find z critical value :

Given Level of Significance = 0.05 and this is right tailed test,

thus find Area = 1 - 0.05 = 0.95

Look in z table for Area = 0.9500 or its closest area and find corresponding z value.

Area 0.9500 is in between 0.9495 and 0.9505 and both the area are at same distance from 0.9500

Thus we look for both area and find both z values

Thus Area 0.9495 corresponds to 1.64 and 0.9505 corresponds to 1.65

Thus average of both z values is : ( 1.64+1.65) / 2 = 1.645

Thus Zc = 1.645

Step 4) Decision rule:

Reject null hypothesis H0, if z test statistic value > z critical value, otherwise we fail to reject H0.

Since z test statistic value = 6.32 > z critical value = 1.645, we reject null hypothesis H0.

Step 5) Conclusion:

Drug A is stronger and preferred by more than 50% of patients.

Thus correct option is:

b. Reject H0; Drug A is stronger and preferred by more than 50% of patients.


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