Question

Compute the standardized test statistic, X. to test the claim o? statistic to the nearest thousandth. 4.3 in 12. s2 -3.6, and a = 0.05. Round the test O A. 18.490 B. 9.209 OC. 0.492 D. 12.961 8. The piston diameter of a certain hand pump is 0.5 inch. The manager determines that the diameters are normally distributed, with a mean of 0.5 inch and a standard deviation of 0.003 inch. After recalibrating the production machine, manager randomly selects 21 pistons and determines that the standard deviation is 0.0022 inch. Is there significant evidence for the manager to conclude that the standard deviation has decreased at the = 0.01 level of significance? What are the correct hypotheses for this test? The null hypothesis is Ho: (1)_o__ (2)_=__(3)_ 0.003 The alternative hypothesis is Hy: (4)_6_ (5) ___<_ () 0:003 Calculate the value of the test statistic x = (Round to two decimal places as needed.) Use technology to determine the P-value for the test statistic. The P-value is (Round to three decimal places as needed.) What is the correct conclusion at the c = 0.01 level of significance? Since the P-value is (7)_arcorter than the level of significance, (8) clonc vcrct the null hypothesis. There (9) is not sufficient evidence to conclude that the standard deviation has decreased at the 0.01 level of significance. (1) O (2) O < (3) O 0.0022. (4) OH (5) O = (6) 0.003. OH = 0.003. G O > 0.0022. оро оооо AV (7) (9) (8) greater less do not reject O reject is not O is

Answer 1

(17)

Correct option:

B.   9.209

Explanation:

ᏋᎭ 602*6 = ve x (1–61) (-) =

(18)

The null hypothesis is H0: $\sigma$ = 0.003

The Alternative Hypothesis is: $\sigma <$ 0.003

2 (n-1) s xổ = G2 (21 - 1) x 0.00222 - = 10.756 0.0032

ndf = n - 1 = 12 - 1 = 11

By Technology, p - value = 0.4639

Since the p value is greater than the level of significance, do not reject the null hypothesis. There is not sufficient evidence to conclude that the standard deviation has decreased at the 0.01 level of significance.