Question

An experiment on the side effects of pain relievers assigned arthritis patients to take one of several over-the-counter pain medications. Of the 440 patients who took one brand of pain reliever, 23 suffered some “adverse symptom.”

(a) If 10% of all patients suffer adverse symptoms, what would be the sampling distribution of the proportion with adverse symptoms in a sample of 440 patients?

(b) Does the experiment provide strong evidence that fewer than 10% of patients who take this medication have adverse symptoms? Verify that the conditions for inference met. State the hypotheses, calculate the test statistic, then obtain and interpret the P-value.

Answer 1

b) The assumption is that sample which is 440 patients drawn from the population and the sampling distribution of sample proportion is approximately normally distributed accordance to central limit theorem. Tsisicaion adverse symptoms is fewer than 10% at 5% significance level. First, give hypothesis, compute test-statistics, p-value then give conclusion based on p- value. The null and alternative hypothesis is Ho : p 0.10 Ha p <0.10 The z-test statistics is,

By using MINITAB, find z-test statistics with the help of following steps: 1) Import the data 2) Select 1 Proportion from Basic Statistics from Stat menu. 3) Enter Summarized data. 4) Click option button choose level of significance and alternative hypothesis. 5) Select Use test and interval based on normal distribution. 6) Click Ok. Test and Cl for One Proportion Test of p = 0.1 vs p < 0.1 958 Upper Sample X N Sample p Bound 2-Value P-Value 23 440 0.052273 0.069726 -3.34 0.000 From the MINITAB output, thez-test statistics is 3.34 The p-value for this test is, From the MINITAB output, thep-value for this test is 0.0001

Decisiorn The conclusion is that pvalue in this context is less than 0.05 which is o, 00o1, so the mull hypothesis is rejected at 5% level of significance. There is sufficient evidence to indicate than 10%. The result is statistically significant.