Question

The gynecology unit of a major hospital in Houston conducted a clinical trial to assess a new drug for preventing low birth weight. Nine pregnant women were randomly chosen to receive the drug and 11 others were randomly chosen to receive a placebo during the 25th week of pregnancy. The 20 birth weights are tabulated below.

Patient ID                        Body weight (lb)

	Drug group	Placebo group
1	6.9	6.4
2	7.6	6.7
3	7.3	5.4
4	7.6	6.9
5	6.8	5.3
6	7.2	6.5
7	8.1	5.9
8	5.5	5.7
9	7.3	7.1
10		5.3
11		7.8

Let µ_dand µ_pbe the mean birth weight for the drug and placebo group, respectively. Perform an appropriate test for H₀ : µ_d= µ_pvs. H_A: µ_d /= µ_pat the 5% level. Please articulate the df and the critical value in your analysis.

Answer 1

The Data provided is:

	Drug group	Placebo group
1	6.9	6.4
2	7.6	6.7
3	7.3	5.4
4	7.6	6.9
5	6.8	5.3
6	7.2	6.5
7	8.1	5.9
8	5.5	5.7
9	7.3	7.1
10		5.3
11		7.8
Count	9	11
Mean	7.1444	6.2727
Standard Deviation	0.7299	0.8235

(1) Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

Ho: ​

Ha:

This corresponds to a two-tailed test, for which a t-test for two population means, with two independent samples, with unknown population standard deviations will be used.

(2) Rejection Region

Based on the information provided, the significance level is α=0.05, and the degrees of freedom are df=18. In fact, the degrees of freedom are computed assuming that the population variances are equal:

Hence, it is found that the critical value for this two-tailed test is tc​=2.101, for α=0.05 and df=18.

The rejection region for this two-tailed test is R={t:∣t∣>2.101}.

(3) Test Statistics

Since it is assumed that the population variances are equal, the t-statistic is computed as follows:

(4) Decision about the null hypothesis

Since it is observed that ∣t∣=2.476>tc​=2.101, it is then concluded that the null hypothesis is rejected.

Using the P-value approach: The p-value is p=0.0234, and since p=0.0234<0.05, it is concluded that the null hypothesis is rejected.

(5) Conclusion

It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that the population mean μ1​ is different than μ2​, at the 0.05 significance level.

Graphically

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