Question

An experiment was planned to compare the mean time (in days) required to recover from a common cold for persons given a daily dose of 4 milligrams (mg) of vitamin C, 142, versus those who were not, H. Suppose that 32 adults were randomly selected for each treatment category and that the mean recovery times and standard deviations for the two groups were as follows. No Vitamin Supplement 32 Sample Size Sample Mean Sample Standard Deviation 4 mg Vitamin C 32 5.3 1.3 6.3 2.7 (a) If you want to show that the use of vitamin C reduces the mean time to recover from a common cold, give the null and alternative hypotheses for the test. O Ho: 041 -2) versus H: 1 - 2) = 0 HO: (4 -) = 0 versus H: (41-42) < 0 Ho: (! -H) < 0 versus H: (M, My) > 0 HO: (441 - 12) = 0 versus H: (41-42) + 0 O MO: (H - 2) = 0 versus H (H - H2) > 0 Is this a one-ar a two-tailed test? one-tailed test two-tailed test (b) Conduct the statistical test of the null hypothesis in part (a) and state your conclusion. Test using a = 0.05. (Round your answer to two decimal places.) Find the test statistic. z = Find the rejection region. (Round your answers to two decimal places. If the test is one-tailed, enter NONE for the unused region.)

Answer 1

Here we have given the mean time of recovery from cold.
- Size - 6.3, Jan Hypotheris Let x and y denote the sample population of mean recovery times o no vikinin supple ment and 4 mg vitamin c respectively, So X and I denota the their respective means and let us ry and no denote their a = 603, 5x = 207 ng = 32, ģ= 5.3, ry=103 caso, the null hypotheris Ho and a nybottelis Ho and alte alternative is given by Nuld Hyloothen's, Hoi Mi=ts Alternative Hypothelis Hoi MzMg of H, : 46-470 So, Hoo My = M2=0 Vis He i or, -M2) >0 Here we see that the alternative hypothel's is right tailed iso, it is a one-tailed (6) So, the text Stectistics is given by z = x- ý Nolo (Under Ho] test
I'll
o z = 6.3-5.3 (27)2 + (1.392 V 32 32 88 0.5297 Z - 188 The critical value of z at Solo level of Significance is 10645 Since the calculated value of z is greata than tabulated value of a , So, we reject null hypotheris and we accept alternative hypothel's. So, we conclude that mean rate of recovery time of no vitamin supplement is greater than mean recovery time of yng vitamin c. . So, the rejection region is given by the graph At /2005 None 220 221.645 NY