Consider the following hypotheses:

H$0$: $\backslash$mu $=450$

HA: $\backslash$mu $!=450$

The population is normally distributed with a population standard deviation of $48.($You may find it useful to reference the appropriate table: z table or t table$)$

a$-1.$ Calculate the value of the test statistic with x$$

$=476$ and n $=75.($Round final answer to $2$ decimal places.$)$

a$-2.$ What is the conclusion at the $5\%$ significance level?

multiple choice $1$

Do not reject H$0$ since the p$-$value is greater than the significance level.

Do not reject H$0$ since the p$-$value is less than the significance level.

Reject H$0$ since the p$-$value is greater than the significance level.

Reject H$0$ since the p$-$value is less than the significance level.

a$-3.$ Interpret the results at $\backslash$alpha

$=0\mathrm{.}05.$

multiple choice $2$

We cannot conclude that the population mean differs from $450.$

We conclude that the population mean differs from $450.$

We cannot conclude that the sample mean differs from $450.$

We conclude that the sample mean differs from $450.$

b$-1.$ Calculate the value of the test statistic with x$$

$=437$ and n $=75.($Negative value should be indicated by a minus sign. Round final answer to $2$ decimal places.$)$

b$-2.$ What is the conclusion at the $1\%$ significance level?

multiple choice $3$

Do not reject H$0$ since the p$-$value is less than the significance level.

Do not reject H$0$ since the p$-$value is greater than the significance level.

Reject H$0$ since the p$-$value is less than the significance level.

Reject H$0$ since the p$-$value is greater than the significance level.

b$-3.$ Interpret the results at $\backslash$alpha

$=0\mathrm{.}01.$

multiple choice $4$

We cannot conclude that the population mean differs from $450.$

We conclude that the population mean differs from $450.$

We cannot conclude that the sample mean differs from $450.$

We conclude that the sample mean differs from $450.$