Question

consider the hypotheses below
$h_0: \mu = 60$
$h_1: \mu < 60$
given that $\bar{x}=53.3$, $s = 11.9$, $n = 30$, and $\alpha=0.10$, complete parts (a) and (b) below
determine the test statistic $t_0$
$t_0=-3.08$
(round to two decimal places as needed.)
what conclusion should be drawn?
a. reject $h_0$. there is not sufficient evidence to conclude that $\mu < 60$
b. reject $h_0$. there is sufficient evidence to conclude that $\mu < 60$
c. do not reject $h_0$. there is not sufficient evidence to conclude that $\mu < 60$
d. do not reject $h_0$. there is sufficient evidence to conclude that $\mu < 60$
b) use technology to determine the p - value for this test
$p - value=$
(round to three decimal places as needed.)

Explanation:

Step1: Determine the degrees of freedom

The degrees of freedom \(df=n - 1\). Given \(n = 30\), so \(df=30 - 1=29\).

Step2: Use the t - distribution to find the p - value

Since the test is left - tailed (\(H_1:\mu\lt60\)) and the test statistic \(t_0=-3.08\).
Using a t - distribution table or technology (e.g., in Excel: =T.DIST(-3.08,29,TRUE)), we calculate the p - value.

Answer:

The p - value is \(0.002\) (rounded to three decimal places).