in experiment was planned to compare the mean time days) required to recover from a common for persons given a daily dose of milligrams (mg) of treatment category and that the mean recovery times and standard deviations for the two groups were as follows. Sample Size Sample Mean Sample Standard Deviation No Vitamin Supplement 34 6.5 2.6 Is this a one- or a two-tailed test? O one-tailed test O two-tailed test (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: (H₂-H₂) = 0 versus H₂: (H₁-H₂) > 0 O Ho: (H₁-H₂) = 0 versus H₂: (₁H₂) = 0 O Ho: (H₁-H₂) = 0 versus H₂: (H₁-H₂) <0 O Ho: (H₂-H₂) <0 versus H₂: (H₁-H₂) >0 O Ho: (H₂-H₂) = 0 versus H₂: (H₁-H₂) = 0 4 mg Vitamin C 34 5.1 1.1 (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. Find the rejection region. (Round your answers to two decimal places. If the test is one-tailed, enter NONE for the unused region.) Conclusion: Ho is rejected. There is insufficient evidence to indicate that Vitamin C reduces the mean recovery time. O Ho is not rejected. There is sufficient evidence to indicate that Vitamin C reduces the mean recovery time. O Ho is not rejected. There is insufficient evidence to indicate that Vitamin C reduces the mean recovery time. OH is rejected. There is sufficient evidence to indicate that Vitamin C reduces the mean recovery time rsus those who were H₂, versus were not, A₁. Suppose that 34 adults were randomly selecte
in experiment was planned to compare the mean time days) required to recover from a common for persons given a daily dose of milligrams (mg) of treatment category and that the mean recovery times and standard deviations for the two groups were as follows. Sample Size Sample Mean Sample Standard Deviation No Vitamin Supplement 34 6.5 2.6 Is this a one- or a two-tailed test? O one-tailed test O two-tailed test (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: (H₂-H₂) = 0 versus H₂: (H₁-H₂) > 0 O Ho: (H₁-H₂) = 0 versus H₂: (₁H₂) = 0 O Ho: (H₁-H₂) = 0 versus H₂: (H₁-H₂) <0 O Ho: (H₂-H₂) <0 versus H₂: (H₁-H₂) >0 O Ho: (H₂-H₂) = 0 versus H₂: (H₁-H₂) = 0 4 mg Vitamin C 34 5.1 1.1 (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. Find the rejection region. (Round your answers to two decimal places. If the test is one-tailed, enter NONE for the unused region.) Conclusion: Ho is rejected. There is insufficient evidence to indicate that Vitamin C reduces the mean recovery time. O Ho is not rejected. There is sufficient evidence to indicate that Vitamin C reduces the mean recovery time. O Ho is not rejected. There is insufficient evidence to indicate that Vitamin C reduces the mean recovery time. OH is rejected. There is sufficient evidence to indicate that Vitamin C reduces the mean recovery time rsus those who were H₂, versus were not, A₁. Suppose that 34 adults were randomly selecte
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![### Vitamin C and Common Cold Recovery: Statistical Analysis
#### Experiment Overview
An experiment was conducted to compare the mean recovery time (in days) for individuals recovering from a common cold. The study focused on two groups: one receiving no vitamin C and the other receiving 4 milligrams (mg) of vitamin C per day. Each group consisted of 34 randomly selected adults. The mean recovery times and standard deviations for the groups were as follows:
| | No Vitamin Supplement | 4 mg Vitamin C |
|--------------------------|-----------------------|----------------|
| Sample Size | 34 | 34 |
| Sample Mean | 6.5 | 5.1 |
| Sample Standard Deviation| 2.6 | 1.1 |
#### Statistical Hypothesis Testing
**(a)** Hypothesis Formulation
To evaluate if vitamin C reduces the recovery time, we set the following hypotheses:
- Null Hypothesis (\(H_0\)): \( \mu_1 - \mu_2 = 0 \)
- Alternative Hypothesis (\(H_a\)): \( \mu_1 - \mu_2 > 0 \)
Where \( \mu_1 \) and \( \mu_2 \) represent the mean recovery times for the no vitamin C group and the vitamin C group, respectively.
This is a **one-tailed test**.
**(b)** Statistical Test Execution
We will conduct a statistical test of the null hypothesis using a significance level (\(\alpha\)) of 0.05.
1. **Find the Test Statistic:**
\[
z =
\]
2. **Determine the Rejection Region:**
If the test is one-tailed, indicate the rejection region:
- \( z > \)
- \( z < \) NONE
3. **Conclusion:**
Select one of the following conclusions based on the test result:
- \(H_0\) is rejected. There is insufficient evidence to indicate that vitamin C reduces the mean recovery time.
- \(H_0\) is not rejected. There is sufficient evidence to indicate that vitamin C reduces the mean recovery time.
- \(H_0\) is not rejected. There is insufficient evidence to indicate that vitamin C reduces the mean recovery time.
- \(H_0\) is rejected. There is sufficient evidence to indicate that vitamin](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbff43673-f06b-43ca-b409-46eb420ace6b%2F6a11e68f-3e84-4b31-bc30-a03e07694610%2Fzfbeel_processed.png&w=3840&q=75)
Transcribed Image Text:### Vitamin C and Common Cold Recovery: Statistical Analysis
#### Experiment Overview
An experiment was conducted to compare the mean recovery time (in days) for individuals recovering from a common cold. The study focused on two groups: one receiving no vitamin C and the other receiving 4 milligrams (mg) of vitamin C per day. Each group consisted of 34 randomly selected adults. The mean recovery times and standard deviations for the groups were as follows:
| | No Vitamin Supplement | 4 mg Vitamin C |
|--------------------------|-----------------------|----------------|
| Sample Size | 34 | 34 |
| Sample Mean | 6.5 | 5.1 |
| Sample Standard Deviation| 2.6 | 1.1 |
#### Statistical Hypothesis Testing
**(a)** Hypothesis Formulation
To evaluate if vitamin C reduces the recovery time, we set the following hypotheses:
- Null Hypothesis (\(H_0\)): \( \mu_1 - \mu_2 = 0 \)
- Alternative Hypothesis (\(H_a\)): \( \mu_1 - \mu_2 > 0 \)
Where \( \mu_1 \) and \( \mu_2 \) represent the mean recovery times for the no vitamin C group and the vitamin C group, respectively.
This is a **one-tailed test**.
**(b)** Statistical Test Execution
We will conduct a statistical test of the null hypothesis using a significance level (\(\alpha\)) of 0.05.
1. **Find the Test Statistic:**
\[
z =
\]
2. **Determine the Rejection Region:**
If the test is one-tailed, indicate the rejection region:
- \( z > \)
- \( z < \) NONE
3. **Conclusion:**
Select one of the following conclusions based on the test result:
- \(H_0\) is rejected. There is insufficient evidence to indicate that vitamin C reduces the mean recovery time.
- \(H_0\) is not rejected. There is sufficient evidence to indicate that vitamin C reduces the mean recovery time.
- \(H_0\) is not rejected. There is insufficient evidence to indicate that vitamin C reduces the mean recovery time.
- \(H_0\) is rejected. There is sufficient evidence to indicate that vitamin
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