Population: Migraine Headaches Sufferers Who Use Depakote

CHAPTER 6 12) Depakote is a medication whose purpose is to reduce the pain associated with migraine headaches. In clinical trials and extended studies of Depakote, 2% of the patients in the study experienced weight gain as a side effect. a) Compute the mean and standard deviation of the random variable X, the number of patients experiencing weight gain in 600 trials of the probability experiment. Population: migraine headaches sufferers who use Depakote Success attribute: Experience weight gain as a side effect n = 600, p = .02 m =n* p = 600*.02 = 12 s =n* p * q = 600*.02*.98 = 11.76 ~ 3.4

b) Would it be unusual to observe 16 or more patients who experience weight gain in a random sample of 600 patients who take the medication? Explain why for each of the following. (i) According to the range rule of thumb [12 – 2*3.4, 12 + 2*3.4] = [5.2, 18.8] It’s usual to observe anywhere from 6 to 18 people experiencing weight gain in groups of 600, so 16 is usual

(ii) To use the probability rule, calculate P(x ≥ 16)  Use methods of chapter 5 to calculate the probability. P(x ≥16) = 1 – binomcdf(600, .02, 15) = .1534 (exact)

Since this probability is higher than 0.05, according to the probability rule, it’s common to observe 16 people experiencing weight gain in groups of 600

 Verify that the normal distribution is appropriate to estimate this probability. Both, n*p and n*q must be greater than or equal to 5

Since n*p = 600*0.02 = 12 and n*q = 600*.98 = 588 Then the normal distribution is appropriate to estimate this probability

 Estimate the probability by using the normal distribution. Use the continuity correction factor. (Note: for large n, the continuity correction factor may not be necessary) Show steps, and then check with calculator feature. Remember to answer the question to the problem.

USE CALCULATOR ONLY for the normal approximation

Normalcdf(15.5,10^9, 12, 11.76 ) = 0.1537 (approximation)

Since this probability is higher than 0.05, according to the probability rule, it’s common to observe 16 people experiencing weight gain in groups of 600 Page 20

2 CHAPTER 6 c) Would it be unusual to observe 21 patients who experience weight gain in a random sample of 600 patients who take the medication? Explain why for each of the following. (i) According to the range rule of thumb [12 – 2*3.4, 12 + 2*3.4] = [5.2, 18.8] It’s usual to observe anywhere from 6 to 18 people experiencing weight gain in groups of 600, so 21 is an unusually high result

(ii) To use the probability rule, calculate P(x ≥ 21)  Use methods of chapter 5 to calculate the probability. 11 P(x ≥21) = 1 – binomcdf(600, .02, 20) = .011 ~ (exact) 1000

Since this probability is lower than 0.05, according to the probability rule, it’s unusual to observe 21 people experiencing weight gain in groups of 600

 Verify that the normal distribution is appropriate to estimate this probability. Both, n*p and n*q must be greater than or equal to 5

Since n*p = 600*0.02 = 12 and n*q = 600*.98 = 588 Then the normal distribution is appropriate to estimate the binomial distribution

 Estimate the probability by using the normal distribution. Use the continuity correction factor. (Note: for large n, the continuity correction factor may not be necessary) Show steps, and then check with calculator feature. Remember to answer the question to the problem. USE CALCULATOR ONLY for the normal approximation

P(x ≥21) = Normalcdf(20.5,10^9, 12, 11.76 ) = 0.007 (approximation)

Since this probability is lower than 0.05, according to the probability rule, it’s unusual to observe 21 people experiencing weight gain in groups of 600. 21 would be a more “common” outcome in a population in which more than 2% experience weight gain as a side effect. That is why we conclude...*****(See ***)

d) The probability that in groups of 600 patients, 21 or more experience weight gain as a side effect is ___.011____ This means, in 1000 trials of this experiment we expect about __11___ trials to result in 21 or more experiencing weight gain. Because this event only happens___11____ out of __1000___ times, we consider it to be usual/unusual

e) If in a random sample of 600 patients who use this medication you actually observe 21 patients who experience weight gain; what might you conclude about the actual percentage of patients who experience weigh gain? (Read rare event rule on page 7) Either something very unusual happened or (****) it may be an indication that, the percentage of Depakote users who experience weight gain as a side effect is actually higher than the posted 2%. Page 21 3