Question

Q1. A new medication for treating virus has shown success in curing the disease for 41 out of 100 patients within a 2 week period. Of patients not receiving the medication, 27% seem to recover within a 2 week period.  

a.) Conduct a hypothesis to see if the medication is making a difference at the .01 significance level

b.) What would the consequences of a Type I and Type 2 error be? Which one would you be at risk for?

Answer 1

(a)

H0: Null Hypothesis:p1 = p2 (The medication is not making a difference)

H0: Null Hypothesis:p1 = p2 (The medication is making a difference) Claim)

n1 = 100

1 = 41/100 = 0.41

'n2 = 100

2 = 27/100 = 0.27

Pooled Proportion is given by:

Test Statistic is given by:

= 0.01

From Table, critical values of Z = 2.58

Since calculated value of Z = 2.09 is less than critical value of Z = 2.58, the difference is not significant. Fail to reject null hypothesis.

Conclusion:
The data do not support the claim that the medication is making a difference.

(b)

Type I Error: Rejection of a true null hypothesis.

Suppose in reality, the medication is not making a difference. But we wrongly conclude that the medication is making a difference. The consequence of making Type I Error is that we will wrongly think that the new medicine will cure the disease and treat the patients with new medicine whereas in reality the new medicine will not cure the disease at all.

Type II Error: Failure to reject a false null hypothesis.

Suppose in reality, the medication is making a difference. But we wrongly conclude that the medication is not making a difference. The consequence of making Type II Error is that we will wrongly think that the new medicine will not cure the disease and we will be failing to treat the patients with new medicine which is very much required.

The consequences of Type I Error are more serious because we will be treating patients with ineffective medicine which will spoil their health further.