Mathematics, 15.10.2020 08:01 garrettbridges6435

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?

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Answer from: NerdyE

0.0028 < p_1 - p_2 < 0.0288

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 n_1 = 3025

The second sample size for placebo is n_2 = 2875

The number of Vioxx users that suffered heart attack is k = 334

The number of non-Vioxx users that suffered heart attack is g = 272

Generally the sample proportion for Vioxx users is mathematically represented as

$\r p_1 = \frac{k}{n_1}$

=> $\r p_1 = \frac{334}{3025}$

=> $\r p_1 = 0.11041$

Generally the sample proportion for placebo users is mathematically represented as

$\r p_2 = \frac{g}{n_2}$

=> $\r p_2 = \frac{272}{2875}$

=> $\r p_2 = 0.09461$

Generally the confidence level is 90% , then the level of significance is $\alpha = (100-90)\%$

=> $\alpha = 0.10$

Generally the critical value of $\frac{\alpha }{2}$ from the normal distribution table is

$Z_{\frac{\alpha }{2} } = 1.645$

Generally the standard error is mathematically represented as

$SE = \sqrt{\frac{\r p_1 (1- \r p_1)}{n_1} + \frac{\r p_2 (1- \r p_2)}{n_2} }$

=> $SE = \sqrt{\frac{0.11041 (1- 0.11041)}{3025} + \frac{0.09461 (1-0.09461)}{2875} }$

=> SE = 0.0079

Generally the margin of error is mathematically represented as

$E= Z_{\frac{\alpha }{2} } * SE$

=> E= 1.645 * 0.0079

=> E= 0.013

Generally the 90% confidence interval is mathematically represented as

0.11041 - 0.09461- 0.013 < p_1 - p_2 < 0.11041 - 0.09461+ 0.013

=> 0.0028 < p_1 - p_2 < 0.0288

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

Answer from: Quest

complete the steps to find the area of the trapezoid.

area of rectangle = 256 square units

area of triangle 1 = 24 square units

area of triangle 2 = 16 square units

area of triangle 3 = 96 square units

area of trapezoid = 120 square units

step-by-step explanation:

Answer from: Quest

$\frac{x}{23.50} = \frac{18\%}{100\%}$ than do 23.50 times 18 and then divide your answer by 100 than you will get x.

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In the early part of this century, the drug company, Merck, produced a powerful non- steroidal anti-...

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