Question

Does taking large doses of vitamin C help prevent the common cold? Five hundred people were randomly selected and divided into two groups. The first group were given large doses of vitamin C and the second were given a placebo. For the vitamin C group, 98 caught a cold over the course of the study. For the placebo group, 112 caught a cold. Perform a hypothesis test to determine whether vitamin C is effective.

(a) Is this an observational study or a randomized experiment? Explain.

(b) State your hypotheses in words and using proper mathematical symbols and notation.

(c) Compute the sample proportions pˆ1 and pˆ2 of those who contracted a cold in the vitamin C group and in the placebo group. Also compute the null value of pˆ.

(d) Compute your test statistic. Round your final answer for the test statistic to two decimal places (but don’t round in the intermediate steps).

(e) Find the p-value using the table in the text.

(f) Is the null hypothesis rejected at α = 0.05? Why or why not? (g) (2 points) State a conclusion in the context of this problem

6. (15 points) Does taking large doses of vitamin C help prevent the common cold? Five hundred people were randomly selected and divided into two groups. The first group were given large doses of vitamin C and the second were given a placebo. For the vitamin C group, 98 caught a cold over the course of the study. For the placebo group, 112 caught a cold. Perform a hypothesis test to determine whether vitamin C is effective. (a) (2 points) Is this an observational study or a randomized experiment? Explain. (b) (2 points) State your hypotheses in words and using proper mathematical symbols and notation. (c) (2 points) Compute the sample proportions P and 2 of those who contracted a cold in the vitamin C group and in the placebo group. Also compute the null value of p. (d) (4 points) Compute your test statistic. Round your final answer for the test statistic to two decimal places (but don't round in the intermediate steps). (e) (2 point) Find the p-value using the table in the text. (1) (1 point) Is the null hypothesis rejected at a = 0.05? Why or why not? (g) (2 points) State a conclusion in the context of this problem.

Answer 1

It is an randomized experimenti selected beroude her soo randomely poeple studicida so - Randomized experiment. we want to test that, Taking large doses of vitamin c help prevent the common colden Pi = Population proportion of people taken large dose of vitamin c & develop calda P2= population propertieñ of people taken placebo k develop cold. in if Pi have less Cold Properties than a Houp, a P2 Vlg. Hai P CP2 Sample 1: Group taken vitamin C sample 2i placeba group opova.

For sample 1, we have that the sample size is N1 = 250, the number of favorable cases is X1 = 98, so then the sample proportion is f1 = * = * = 0.392 For sample 2, we have that the sample size is N2 = 250, the number of favorable cases is X2 = 112, so then the sample proportion is P2 = x = 232 = 0.448 The value of the pooled proportion is computed as p= 4.1* X:+X2 = 98-112 = 0.42 on is computed as P N1-N2 = 250-250 Vis Also, the given significance level is a = 0.05.

(d) Test Statistics The Z-statistic is computed as follows: 2 = P1 - 2 (1-)(1/nı +1/12) 0.392 -0.448 0.42. (1 – 0.42)(1/250 +1/250) = -1.269

P-vale - - ztreco, el P(Z <2) P(Z < -10 209) Ź or 1023 p-vane [001023

L=oot, p-valer =023 20.05 we fail to reject Hool we may corelude that the deeta do not provide suficient eridone to suppast claim that taking large doel of vitamin C prevent cold.