Question

To combat the novel coronavirus (COVID-10) pandemic, the Bloomington Pharmaceutical Co. Ltd. aggressively conducted a clinical trial with 8 patients for its new drug Remdiessivir. Patient’s health condition was evaluated before and after receiving the medication with a rating system in which 10 points represents complete recovery and 1 for being the worst condition. (a) Use the collected data below to assess the efficacy of the drug by conducting a hypothesis test at 5% significance level.

8	7
9	9
3	6
4	6
2	7
7	5
4	10
8	6

Answer 1

(1) Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

Ho: μD​ = 0

Ha: μD​ ≠ 0

This corresponds to a two-tailed test, for which a t-test for two paired samples be used.

(2) Rejection Region

Based on the information provided, the significance level is α=0.05, and the degrees of freedom are df=7.

Hence, it is found that the critical value for this two-tailed test is tc​=2.365, for \α=0.05 and df=7.

The rejection region for this two-tailed test is R={t:∣t∣>2.365}.

(3) Test Statistics

The t-statistic is computed as shown in the following formula:

(4) Decision about the null hypothesis

Since it is observed that ∣t∣=1.249≤tc​=2.365, it is then concluded that the null hypothesis is not rejected.

Using the P-value approach: The p-value is p=0.2518, and since p=0.2518≥0.05, it is concluded that the null hypothesis is not rejected.

(5) Conclusion: It is concluded that the null hypothesis Ho is not rejected. Therefore, there is not enough evidence to claim that the population mean μ1​ is different than μ2​, at the 0.05 significance level. We don't have sufficient evidence to show that new drug Remdiessivir. has an effect at 0.05 level of significance.