To test $H_0: \sigma = 47$ versus $H_1: \sigma < 47$, a random sample of size $n = 25$ is obtained from a population that is known to be normally distributed. Complete parts (a) through (c).
Click the icon to view the chi-square distribution table.
(a) If the sample standard deviation is determined to be $s = 40.3$, compute the test statistic.
$\chi^2_0 = $ (Round to two decimal places as needed.)
(b) If the researcher decides to test this hypothesis at the $\alpha = 0.05$ level of significance, approximate the P-value.
The P-value is
(c) Will the researcher reject the null hypothesis? Why?
A. The P-value is less than the $\alpha = 0.05$ level of significance, so the researcher will not reject the null hypothesis.
B. The P-value is greater than the $\alpha = 0.05$ level of significance, so the researcher will not reject the null hypothesis.
C. The P-value is less than the $\alpha = 0.05$ level of significance, so the researcher will reject the null hypothesis.
D. The P-value is greater than the $\alpha = 0.05$ level of significance, so the researcher will reject the null hypothesis.
