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/ principles stats w HW 7: Problem 9 Previous Problem Problem ListNext Problem (1 point) Physicians at a clinic gave what they thought were drugs to 980 asthma, ulcer, and herpes patients. Although the doctors later leamed that the drugs were really placebos, 56 % of the patients reported an improved condition. Assume that if the placebo is ineffective, the probability of a patients condition improving is 0.52. For the hypotheses that the proportion of improving is 0.52 against that it is >0.52, find the p-value. Preview My Answers Submit A You have attempted this problem 1 time. Your overall recorded score is 0%. You have unlimited attempts remainingExplanation / Answer
Solution:- p-value = 0.06
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: P < 0.52
Alternative hypothesis: P > 0.52
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 ]
= 0.01596
z = (p - P) /
z = - 2.51
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 less than - 2.51.
Thus, the P-value = 0.006
Interpret results. Since the P-value (0.006) is less than the significance level (0.05), we cannot accept the null hypothesis.
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