Question

In a study of the effectiveness of a new pain killer, 46 out of 821 patients tested reported experiencing side effects. Use a a = 0.01 significance level to determine if the proportion who side effects from this drug is lower than the 7.8% rate of side effects for the older version of this medication.

Answer 1

Solution:

Given:

n = 821

x = 46

Sample proportion is:

We have to test if the proportion who side effects from this drug is lower than the 7.8% rate of side effects for the older version of this medication.

Step 1) State H0 and H1:

H0 : p =0.078

Vs

H1: p < 0.078

Step 2) Test statistic::

Step 3) Find z critical value using 0.01 significance level

Since this is left tailed test , look in z table for area = 0.0100 or its closest area and find z value.

Area 0.0099 is closest to 0.0100 and it corresponds to -2.3 and 0.03

thus z critical value = -2.33

Step 4) Decision Rule:
Reject null hypothesis ,if z  test statistic value < z critical value = -2.33 , otherwise we fail to reject H0.

Since z test statistic value = -2.35 < z critical value = -2.33, we reject null hypothesis H0.

Step 5) Conclusion:

At 0.01 significance level there is sufficient evidence to conclude that: the proportion who side effects from this drug is lower than the 7.8% rate of side effects for the older version of this medication.