# 1. Is there evidence of diffetence in mean time spent exercising between males and females? In the sample, we have a mean of 12.4 hours a week for 20 males and a mean of 9.4 hours a week for 30 females. 2. Is there evidence of a negative correlation between blood pressure and heart rate? In a sample of 200 2. Is there patients, we found a sample correlation of -0.057.

1. Is there evidence of diffetence in mean time spent exercising between males and females? In the sample, we have a mean of 12.4 hours a week for 20 males and a mean of 9.4 hours a week for 30 females.
2. Is there evidence of a negative correlation between blood pressure and heart rate? In a sample of 200 2. Is there patients, we found a sample correlation of -0.057.
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Null Hypothesis ${H}_{0}\left({P}_{1}={P}_{2}\right)$
Alternative Hypothesis ${H}_{1}\left({P}_{1}<{P}_{2}\right)$
${n}_{1}=20\phantom{\rule{0ex}{0ex}}{P}_{1}=12.4\phantom{\rule{0ex}{0ex}}{n}_{2}=30\phantom{\rule{0ex}{0ex}}{P}_{2}=9.4\phantom{\rule{0ex}{0ex}}P=\frac{{n}_{1}{P}_{1}+{n}_{2}{P}_{2}}{{n}_{1}+{n}_{2}}\phantom{\rule{0ex}{0ex}}=\frac{20×12.4+30×9.4}{20+30}\phantom{\rule{0ex}{0ex}}=10.6$
Expected value of $\left({P}_{1}-{P}_{2}\right)$ is 0 and
S.E of ${P}_{1}-{P}_{2}=\sqrt{pq\left(\frac{1}{{n}_{1}}+\frac{1}{{n}_{2}}\right)}\phantom{\rule{0ex}{0ex}}=\sqrt{12.4×9.4\left(\frac{1}{20}+\frac{1}{30}\right)}\phantom{\rule{0ex}{0ex}}=3.116\phantom{\rule{0ex}{0ex}}Z=\frac{{P}_{1}-{P}_{2}}{S.E}=\frac{12.4-9.4}{3.1166}\phantom{\rule{0ex}{0ex}}=0.962587$
P value $\to 0.167879$ (onetailed)
The result is not significant at P<0.05
2. t test=$\sqrt[r]{\frac{n-2}{1-{r}^{2}}}$
$\sqrt[-0.057]{\frac{200-2}{1-\left(-0.057{\right)}^{2}}}\phantom{\rule{0ex}{0ex}}=-0.803367$
P value is 0.21138 (onetailed)
The result is not sihnificant at P <0.05