An old medical textbook states that the mean sodium level for healthy adults is $142$mEq per liter of blood. A medical researcher believes that, because of modern dietary habits, the mean sodium level for healthy adults, $,$ now differs from that given in the textbook. A random sample of $80$ healthy adults is evaluated. The mean sodium level for the sample $140$mEq per liter of blood. It is known that the population standard deviation of adult sodium levels is $14$mEq. Can we conclude, at the $0\mathrm{.}05$ level of significance, that the population mean adult sodium level differs from that given in the textbook?

Perform a two$-$tailed test. Then complete the parts below.

Carry your intermediate computations to three or more decimal places, and round your responses as specified below. $($If necessary, consult a list of formulas.$)$

$($a$)$ State the null hypothesis $H_0$ and the alternative hypothesis $H_1$

$H_0$:$$

$H_1$:$$

$($b$)$ Determine the type of test statistic to use.

$($c$)$ Find the value of the test statistic. $($Round to three or more decimal places.$)$

$($d$)$ Find the p$-$value. $($Round to three or more decimal places.$)$

$($e$)$ Can we conclude that the population mean adult sodium level differs from that given in the textbook?

Yes No