1· The Dow Jones Industrial Average closing prices for the bull market 1982-1986
ID: 3051183 • Letter: 1
Question
1· The Dow Jones Industrial Average closing prices for the bull market 1982-1986 were examined. Out of the 1112 trading days in that period, the average increased on 573 days. Is the Dow just as likely to increase as it is to decrease on any given day? Arthritis is a painful, chronic inflammation of the joints. An experiment on the side effects of pain relievers examined arthritis patients to find the proportion of patients who suffer side effects when using ibuprofen to relieve the pain. If more than 3% of users suffer side effects, the Food and Drug Administration will put a stronger warning label on packages of ibuprofen. Of the 440 subjects with chronic arthritis that were given ibuprofen for pain relief; 23 subjects suffered from adverse side effects. Does the FDA need to put a stronger warning label on packages of ibuprofen? 2.Explanation / Answer
Solution:-
2)
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: P < 0.03
Alternative hypothesis: P > 0.03
Note that these hypotheses constitute a one-tailed test. The null hypothesis will be rejected only if the sample proportion is too small.
Formulate an analysis plan. For this analysis, the significance level is 0.05. The test method, shown in the next section, is a one-sample z-test.
Analyze sample data. Using sample data, we calculate the standard deviation () and compute the z-score test statistic (z).
= sqrt[ P * ( 1 - P ) / n ]
= 0.008132
z = (p - P) /
z = 2.74
where P is the hypothesized value of population proportion in the null hypothesis, p is the sample proportion, and n is the sample size.
Since we have a one-tailed test, the P-value is the probability that the z-score is more than 2.74. We use the Normal Distribution Calculator to find P(z > 2.74).
Thus, the P-value = 0.0031.
Interpret results. Since the P-value (0.0031) is less than the significance level (0.05), we haave to accept the null hypothesis.
From above test we have sufficiet evidence that more than 3% of usrs suffer side effects.
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