Question

you wish to test the following claim ($h_a$) at a significance level of $\alpha = 0.001$.
$h_o: \mu = 90.7$
$h_a: \mu \
eq 90.7$
you believe the population is normally distributed, but you do not know the standard deviation. you obtain a sample of size $n = 16$ with a mean of $m = 86.7$ and a standard deviation of $sd = 10.7$.
what is the critical value for this test? (report answer accurate to three decimal places.)
critical value $=\pm$
what is the test statistic for this sample? (report answer accurate to three decimal places.)
test statistic $=$
the test statistic is...
$\bigcirc$ in the critical region
$\bigcirc$ not in the critical region
this test statistic leads to a decision to...
$\bigcirc$ reject the null
$\bigcirc$ accept the null
$\bigcirc$ fail to reject the null

Explanation:

Step1: Determine the degrees of freedom

The degrees of freedom \(df=n - 1\). Given \(n = 16\), so \(df=16-1 = 15\).

Step2: Find the critical value

Since \(\alpha=0.001\) and it is a two - tailed test, we look up the \(t\) - value in the \(t\) - distribution table. For \(df = 15\) and \(\alpha/2=0.0005\), the critical value \(t_{\alpha/2,df}\) is \(t_{0.0005,15}\approx\pm3.733\)

Answer:

The critical value is \(\pm3.733\)