Question

consider the hypotheses below
$h_0: \mu = 60$
$h_1: \mu < 60$
given that $\overline{x}=53.3$, $s = 11.9$, $n = 30$, and $\alpha=0.10$, complete parts (a) and (b) below
determine the critical value(s)
the critical value(s) is(are)
(round to three decimal places as needed. use a comma to separate answers as needed)
determine the test statistic $t_0$
$t_0=$
(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

Explanation:

Step1: Determine the critical value

Since it is a left - tailed test with \(n = 30\) (degrees of freedom \(df=n - 1=29\)) and \(\alpha = 0.10\).
Using the t - distribution table or a calculator, the critical value \(t_{\alpha,df}=t_{0.10,29}=- 1.311\)

Step2: Calculate the test statistic \(t_0\)

The formula for the t - test statistic is \(t_0=\frac{\bar{x}-\mu}{s/\sqrt{n}}\)
Given \(\bar{x}=53.3\), \(\mu = 60\), \(s = 11.9\), \(n = 30\)

$$
LATEXBLOCK0
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Step3: Make a decision

Since \(t_0=-3.08\lt t_{\alpha}=-1.311\), we reject the null hypothesis \(H_0\)

Answer:

• The critical value is \(-1.311\)
• The test statistic \(t_0=-3.08\)
• The conclusion is B. Reject \(H_0\). There is sufficient evidence to conclude that \(\mu\lt60\)