tian method to produce steel rods. A random somple 2. In a clinical study of an
ID: 2947015 • Letter: T
Question
tian method to produce steel rods. A random somple 2. In a clinical study of an allergy drug, 108 of the 202 subjects reported experiencing significant relief from their symptoms. At the 0.01 significance level, test the claim that h more than half of all those using the drug experience relief Opposite: D Test Statistie pd 650.9 0. 03517 202 202 Critical Value(s) or P-Value pvalUCE O. Critical value 8389 a345 -?, Graph with test statistic and critical value marked clearly Circle One: Reject Ho Fail to Reject H Conclusion:Explanation / Answer
Solution:-
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: P < 0.50
Alternative hypothesis: P > 0.50
Note that these hypotheses constitute a one-tailed test.
Formulate an analysis plan. For this analysis, the significance level is 0.01. 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 (S.D) and compute the z-score test statistic (z).
S.D = sqrt[ P * ( 1 - P ) / n ]
S.D = 0.03518
z = (p - P) / S.D
z = 0.985
zcritical = 2.327
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 greater than 0.985.
Thus, the P-value = 0.162.
Interpret results. Since the P-value (0.162) is greater than the significance level (0.01), we have to accept the null hypothesis.
Fail to reject H0.
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