When a poultry farmer uses his regular feed, the newborn chickens have normally distributed weights with a mean of $62\mathrm{.}4oz.$ In an experiment with an enriched feed mixture, ten chickens are born with the following weights $($in ounces$).$

$64,64\mathrm{.}6,66\mathrm{.}6,64\mathrm{.}4,62\mathrm{.}6,64\mathrm{.}4,66,65\mathrm{.}4,67\mathrm{.}1,65\mathrm{.}7$

Use the $=0\mathrm{.}01$ significance level to test the claim that the mean weight is higher with the enriched feed.

$($a$)$ The sample mean is $\stackrel{}{x}=$

$($b$)$ The sample standard deviation is $s=$

$($c$)$ The test statistic is $t=$

$($d$)$ The critical value is $t^{**}=$

$($e$)$ The conclusion is

A$.$ There is not sufficient evidence to support the claim that with the enriched feed, the mean weight is greater than $62\mathrm{.}4.$

B$.$ There is sufficient evidence to support the claim that with the enriched feed, the mean weight is greater than $62\mathrm{.}4.$