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, 2, versus those who were not, 1. 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 4 mg
Vitamin C
Sample Size 32 32
Sample Mean 6.5 5.3
Sample Standard Deviation 2.7 1.4
(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.
- H0: (1 − 2) < 0 versus Ha: (1 − 2) > 0
- H0: (1 − 2) ≠ 0 versus Ha: (1 − 2) = 0
- H0: (1 − 2) = 0 versus Ha: (1 − 2) ≠ 0
- H0: (1 − 2) = 0 versus Ha: (1 − 2) < 0
- H0: (1 − 2) = 0 versus Ha: (1 − 2) > 0
Is this a one- or 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
= 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.)
z >
z <
Conclusion:
- H0 is not rejected. There is insufficient evidence to indicate that Vitamin C reduces the mean recovery time.
- H0 is rejected. There is sufficient evidence to indicate that Vitamin C reduces the mean recovery time.
- H0 is rejected. There is insufficient evidence to indicate that Vitamin C reduces the mean recovery time.
- H0 is not rejected. There is sufficient evidence to indicate that Vitamin C reduces the mean recovery time.