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 mg of vitamin C, μ₂, versus those who were not given a vitamin supplement, μ₁. Suppose that 34 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	34	34
Sample mean	6.1	5.1
Sample standard deviation	2.4	1.9

(a) Suppose your research objective is to show that the use of vitamin C reduces the mean time required to recover from a common cold and its complications. Give the null and alternative hypotheses for the test.

H₀: (μ₁ − μ₂) = 0 versus H_a: (μ₁ − μ₂) ≠ 0

H₀: (μ₁ − μ₂) < 0 versus H_a: (μ₁ − μ₂) > 0   

H₀: (μ₁ − μ₂) = 0 versus H_a: (μ₁ − μ₂) > 0

H₀: (μ₁ − μ₂) ≠ 0 versus H_a: (μ₁ − μ₂) = 0

H₀: (μ₁ − μ₂) = 0 versus H_a: (μ₁ − μ₂) < 0

Is this a one- or a two-tailed test?

(b) Conduct the statistical test of the null hypothesis in part (a) and state your conclusion. Test using

α = 0.05.

(Round your answers to two decimal places.)
z =

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.    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.

Answer 1

For No vitamin supplement :

x̅1 = 6.1, σ1 = 2.4, n1 = 34

For 4 mg Vitamin C :

x̅2 = 5.1, σ2 = 1.9, n2 = 34

a) Null and alternative hypotheses for the test.

H0: (μ1 − μ2) = 0 versus Ha: (μ1 − μ2) > 0

b) Test statistic:

z = (x̅1 - x̅2)/√(σ1²/n1 + σ2²/n2 ) = (6.1 - 5.1)/√(2.4²/34 + 1.9²/34) = 1.90

p-value :

p-value =1- NORM.S.DIST(1.9049, 1) = 0.0284

H₀ is rejected. There is sufficient evidence to indicate that Vitamin C reduces the mean recovery time.