In the early part of this century, the drug company, Merck, produced a powerful non- steroidal anti-inflammatory drug (NSAID) known as Vioxx. Vioxx was very effective in reducing pain due to arthritis and, unlike some NSAIDs, did not cause digestive system or liver problems. However, a couple of years after Vioxx was introduced to the market, some independent studies showed a possible connection between NSAIDs and increased risk of heart attack in the elderly. Since many arthritis sufferers (and many Vioxx users) are elderly, these studies were a cause of concern.

To test whether this was the case for Vioxx, Merck conducted a large-scale study in which 3025 randomly selected elderly Vioxx users were put on the drug while 2875 were given a placebo. The volunteers were monitored for 18 months. During this time, 334 of the Vioxx group members and 272 members of the placebo group suffered heart attacks.

Required:
a. Compute by hand a 90% confidence interval for the difference in heart attack risk between Vioxx users and non-Vioxx users (the placebo group.)
b. Interpret the interval. What action does it suggest should be taken regarding Vioxx?

The interval means that there is 90% confidence that the true difference between the proportion of Vioxx users who suffered from heart attack and the non-Vioxx users (the placebo group ) who suffered from heart attack lie within the interval

The use of Vioxx drug should be stopped

Step-by-step explanation:

From the question we are told that

The sample size for Vioxx users is [tex]n_1 = 3025[/tex]

The second sample size for placebo is [tex]n_2 = 2875[/tex]

The number of Vioxx users that suffered heart attack is [tex]k = 334[/tex]

The number of non-Vioxx users that suffered heart attack is [tex]g = 272[/tex]

Generally the sample proportion for Vioxx users is mathematically represented as

[tex]\r p_1 = \frac{k}{n_1}[/tex]

=> [tex]\r p_1 = \frac{334}{3025}[/tex]

=> [tex]\r p_1 = 0.11041 [/tex]

Generally the sample proportion for placebo users is mathematically represented as

[tex]\r p_2 = \frac{g}{n_2}[/tex]

=> [tex]\r p_2 = \frac{272}{2875}[/tex]

=> [tex]\r p_2 = 0.09461 [/tex]

Generally the confidence level is 90% , then the level of significance is [tex]\alpha = (100-90)\%[/tex]

=> [tex]\alpha = 0.10[/tex]

Generally the critical value of [tex]\frac{\alpha }{2}[/tex] from the normal distribution table is

[tex]Z_{\frac{\alpha }{2} } = 1.645[/tex]

Generally the standard error is mathematically represented as

[tex]SE = \sqrt{\frac{\r p_1 (1- \r p_1)}{n_1} + \frac{\r p_2 (1- \r p_2)}{n_2} }[/tex]

=> [tex]SE = \sqrt{\frac{0.11041 (1- 0.11041)}{3025} + \frac{0.09461 (1-0.09461)}{2875} }[/tex]

=> [tex]SE = 0.0079[/tex]

Generally the margin of error is mathematically represented as

[tex] E= Z_{\frac{\alpha }{2} } * SE[/tex]

=> [tex] E= 1.645 * 0.0079[/tex]

=> [tex] E= 0.013[/tex]

Generally the 90% confidence interval is mathematically represented as

[tex]0.11041 - 0.09461- 0.013 < p_1 - p_2 < 0.11041 - 0.09461+ 0.013 [/tex]

=> [tex]0.0028 < p_1 - p_2 < 0.0288[/tex]

The interval means that there is 90% confidence that the true difference between the proportion of Vioxx users who suffered from heart attack and the non-Vioxx users (the placebo group ) lie within the interval

Looking at the interval we see that proportion of Vioxx users who suffered is more compared to non-Vioxx users (the placebo group )[i.e the both limit of the interval is positive ] hence the use of Vioxx drug should be stopped