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 that32adults 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

Supplement4 mg

Vitamin CSample Size3232Sample Mean6.75.5Sample Standard Deviation2.81.4(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: (₁₂)0 versusH_a: (₁₂) = 0

H₀: (₁₂) = 0 versusH_a: (₁₂) > 0

H₀: (₁₂) = 0 versusH_a: (₁₂)0

H₀: (₁₂) < 0 versusH_a: (₁₂) > 0

H₀: (₁₂) = 0 versusH_a: (₁₂) < 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:

H₀is rejected. There is insufficient evidence to indicate that Vitamin C reduces the mean recovery time.

H₀is rejected. There is sufficient evidence to indicate that Vitamin C reduces the mean recovery time.

H₀is not rejected. There is insufficient evidence to indicate that Vitamin C reduces the mean recovery time.

H₀is not rejected. There is sufficient evidence to indicate that Vitamin C reduces the mean recovery time.