In: Math
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.
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.