Question

question 4 of 8, step 2 of 3
a pharmaceutical company needs to know if its new cholesterol drug, praxor, is effective at lowering cholesterol levels. it believes that people who take praxor will average a greater decrease in cholesterol level than people taking a placebo. after the experiment is complete, the researchers find that the 44 participants in the treatment group lowered their cholesterol levels by a mean of 20.7 points with a standard deviation of 5.1 points. the 34 participants in the control group lowered their cholesterol levels by a mean of 18.6 points with a standard deviation of 1.3 points. assume that the population variances are not equal and test the companys claim at the 0.02 level. let the treatment group be population 1 and let the control group be population 2.
step 2 of 3: compute the value of the test statistic. round your answer to three decimal places.
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Explanation:

Step1: Identify the formula for two - sample t - test with unequal variances

The formula for the two - sample t - test statistic when population variances are unequal is $t=\frac{(\bar{x}_1-\bar{x}_2)-(\mu_1 - \mu_2)}{\sqrt{\frac{s_1^{2}}{n_1}+\frac{s_2^{2}}{n_2}}}$. Here, we assume $\mu_1-\mu_2 = 0$ (null hypothesis), $\bar{x}_1$ is the sample mean of treatment group, $\bar{x}_2$ is the sample mean of control group, $s_1$ is the sample standard deviation of treatment group, $s_2$ is the sample standard deviation of control group, $n_1$ is the sample size of treatment group and $n_2$ is the sample size of control group.

Step2: Substitute the given values

We have $\bar{x}_1 = 20.7$, $\bar{x}_2=18.6$, $s_1 = 5.1$, $s_2 = 1.3$, $n_1 = 44$, $n_2=34$.
\[

$$\begin{align*} t&=\frac{(20.7 - 18.6)-0}{\sqrt{\frac{5.1^{2}}{44}+\frac{1.3^{2}}{34}}}\\ &=\frac{2.1}{\sqrt{\frac{26.01}{44}+\frac{1.69}{34}}}\\ &=\frac{2.1}{\sqrt{0.591136 + 0.049706}}\\ &=\frac{2.1}{\sqrt{0.640842}}\\ &=\frac{2.1}{0.800526}\\ &\approx2.623 \end{align*}$$

\]

Answer:

$2.623$