Question

quarters are currently minted with weights normally distributed and having a standard deviation of 0.066. new equipment is being tested in an attempt to improve quality by reducing variation. a simple random sample of 28 quarter is obtained from those manufactured with the new equipment, and this sample has a standard deviation of 0.044. use 0.05 significance level to test the claim that quarters manufactured with the new equipment have weights with a standa deviation less than 0.066. does the new equipment appear to be effective in reducing the variation of weights?
c. $h_0: \sigma \geq 0.066$; $h_a: \sigma < 0.066$ (claim)
d. $h_0: \sigma \leq 0.066$ (claim); $h_a: \sigma > 0.066$
(b) find the critical value(s).
$\chi_0^2 = 16.151$
(use a comma to separate answers as needed. round to three decimal places as needed.)
identify the rejection region(s).
a.
b.
c.

Explanation:

For a left - tailed test (since the alternative hypothesis \(H_{a}:\sigma< 0.066\)), the rejection region is in the left - tail of the \(\chi^{2}\) distribution. Option A shows the shaded region (rejection region) in the left - tail, which is consistent with a left - tailed test for the chi - square test of variance. Option B shows the non - rejection region in the left - tail and Option C shows a two - tailed rejection region, which is not appropriate for this left - tailed test.

Answer:

A