experiment was conducted to determine if a daily dose of 1,000 milligrams of Vit

Question

experiment was conducted to determine if a daily dose of 1,000 milligrams of Vitamin Cis effective in reducing the probability of getting a cold. Group 1 consisted of 238 people who took the vitamin daily for six months. Of this group, 42 had at least one cold during the period. Group 2 consisted of 241 people who took a placebo every day for six months. Of this group, 61 had at least one cold during the period a. Conduct a hypothesis test to determine whether there is statistical evidence to conclude that Vitamin C is effective in reducing the probability of getting a cold. Be sure to include your hypotheses, the p-value, the point estimates, the test statistic, and an interpretation of your results in your response Construct a 95% confidence interval for the difference in proportion of people who will get at least one cold if they take Vitamin C. Be sure to interpret interval in your response Discuss the advantages and disadvantages of both hypothesis tests and confidence intervals in conveying important information related to this study b. c.

Explanation / Answer

H0 : Proportion of people in group 1 (Vitamin C) who had at least one cold during the period is same as propotion of people in group 2 (Placebo) who had at least one cold during the period. pC = pplacebo

Ha : Proportion of people in group 1 (Vitamin C) who had at least one cold during the period is less then the propotion of people in group 2 (Placebo) who had at least one cold during the period. pC < pplacebo

Point estimate for

p^C = 42/238 = 0.1765

pplacabo = 61/241 = 0.2531

Pooled estimate p0 = (42 + 61)/ (238 + 241) = 0.215

Stanard error of the difference in propotion se0 = sqrt[p0 * (1-po) * (1/n1+ 1/n2)] = sqrt[0.215 * 0.785 * (1/238 + 1/241)]

= 0.0375

Test Statistic

Z = (p^C -p^placabo)/se0 = (0.1735 - 0.2531)/ 0.0375 = - 2.12

p- value = Pr(Z < -2.12) = 0.0170

so that is less than the 0.05 confidenceinterval which tell that we shall reject the null hypothesis and can conclude that Vitamin C has an effect on the Cold.

(b) 95% confidence interval = (p^C -p^placabo) +- Z95% se0

= (0.1735 - 0.2531) +- 1.96 * 0.0375

= (-0.1531, -0.0061)

so we can say that there is 95% chance or probability that differrence in proportion of people who will get at least one cold will be inbetwwen 0.1531 and 0.0061.

(c) Hypothesis testing are advantegous as it provides a p- values which tells us the probability of that event happening like there would be 0.017 probability that there be no mean difference in proportion.

Hypothesis testing relates to a single conclusion of statistical significance vs. no statistical significance. Whereas, Confidence intervals provide a range of plausible valuesfor your population. That makes it advantages for confidence interval. We Use hypothesis testing when you want to do a strict comparison with a pre-specified hypothesis and significance level. we use confidence intervals to describe the magnitude of an effect (e.g., mean difference, odds ratio, etc.) or when we want to describe a single sample.

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