We wish to determine if height of sons is increasing over that of the fathers. After creating a data set height of sons$-$height of fathers we compute the mean and standard deviation. Sample mean of the differenced data: $$d $=0\mathrm{.}32$ and sample standard deviation of the differenced data : sd $=2\mathrm{.}89.$

$($a$)$ How many samples do we have.

$($b$)$ If there are two samples are they independent of dependent?

$($c$)$ What is the parameter type?

$($d$)$ What is the null hypothesis? Explain your reasoning $($e$)$ What is the alternative hypothesis? Explain your reasoning. $($f$)$ Is your test two$-$tailed, left$-$tailed or right$-$tailed? $($g$)$ What is the level of significance $\backslash$alpha $?$

$($h$)$ What is the test statistic?

$($i$)$ Do we reject the null or fail to reject the null.

$($j$)$ Interpret your result.