To test $H_0: \mu = 60$ versus $H_1: \mu < 60$, a random sample of size $n = 24$ is obtained from a population that is known to be normally distributed. Complete parts (a) through (d) below.
(a) If $\bar{x} = 57.6$ and $s = 10.1$, compute the test statistic.
$t_0 = \text{____}$ (Round to three decimal places as needed.)
(b) If the researcher decides to test this hypothesis at the $\alpha = 0.1$ level of significance, determine the critical value(s). Although technology or a t-distribution table can be used to find the critical value, in this problem use the t-distribution table given.
Critical Value: $\text{____}$ (Round to three decimal places. Use a comma to separate answers as needed.)
(c) Draw a t-distribution that depicts the critical region. Choose the correct answer below.
(d) Will the researcher reject the null hypothesis?
A. No, because the test statistic does not fall in the critical region.
B. No, because the test statistic falls in the critical region.
C. Yes, because the test statistic does not fall in the critical region.
D. Yes, because the test statistic falls in the critical region.
