(Solved): Assume that you have a sample of n1=7, with the sample mean X1=42, and a sample standard d ...

Assume that you have a sample of $$n_1=7$$, with the sample mean $${\stackrel{?}{X}}_1=42$$, and a sample standard deviation of $$S_1=4$$, and you have an independent sample of $$n_2=4$$ from another population with a sample mean of $${\stackrel{?}{X}}_2=39$$ and the sample standard deviation $${\mathrm{S}}_2=5$$. Assuming the population variances are equal, at the 0.01 level of significance, is there evidence that $${?}_1>{?}_2$$ ? Determine the hypotheses. Choose the correct answer below. A. $${\mathrm{H}}_0:{?}_1?={?}_2$$ B. $${\mathrm{H}}_0:{?}_1>{?}_2$$ $${\mathrm{H}}_1:{?}_1={?}_2$$ $$H_1:{?}_1?{?}_2$$ c. $$H_0:{?}_1={?}_2$$ D. $${\mathrm{H}}_0?{?}_1?{?}_2$$ $$H_1:{?}_1?={?}_2$$ $$H_1:{?}_1>{?}_2$$ Find the test statistic. The value of the test statistic $$=$$ (Round to 4 decimal places as needed.) Find the $$p$$-value. $$p$$-value $$=$$ (Round to four decimal places as needed.) Choose the correct conclusion below. A. Reject $$H_0$$. There is sufficient evidence that $${?}_1>{?}_2$$. B. Do not reject $$H_0$$. There is insufficient evidence that $${?}_1>{?}_2$$. C. Do not reject $$H_0$$. There is sufficient evidence that $${?}_1>{?}_2$$. D. Reject $$H_0$$. There is insufficient evidence that $${?}_1>{?}_2$$.