Question

SELECT ALL APPLICABLE CHOIC B) There is NOT enough evidence to reject the Ho Hį: 0=3.5 (claim) H: 0 #3.5 Assume that a simple random sample has been selected from a normally distributed population and test the given claim. State the final conclusion that addresses the original claim and select four correct choices. A manufacturer uses a new production method to produce steel rods. A random sample of 17 steel rods resulted in lengths with a standard deviation of 2.1 cm. At the 0.10 significance level, test the claim that the new production method has lengths with a standard deviation different from 3.5 cm, which was the standard deviation for the old method. C) Test statistic: x2 = 5.760 . Critical values: x2 = 7.962, 26.296 D) There is enough evidence to support the Claim E) There is enough evidence to reject the Ho F) Test statistic: x² = 8.760. Critical values: x² = 9.962, 16.296 G) There is NOT enough evidence to support the Claim H) Hų: 03.5 (claim) Ho: 0= 3.5 I) None of these

Answer 1

From the given information

n =17

s=2.1

$\sigma$=3.5

G) Null and alternative hypothesis

HO: 0 = 3.5U/sH1:0 +3.5(claim)

C) Under null hypothesis

Test statistic is

$\chi^2$ = = 16*2.1*2.1/(3.5*3.5) = 5.76

(n-1)*8210

Critical value = $\chi^2$ _{alpha/2, n-1}  and $\chi^2$ _{1-(alpha/2),n-1}

_Alpha=0.1

$\chi^2$_0.05,16 = 7.9616 = 7.962

$\chi^2$_0.95,16 = 26.2963 = 26.296

E) Test statistic

5.76 (test statistic) < 7.962 (lower critical value

Hence we reject the null hypothesis at 0.1 level of significance

D) Hence we conclude that there is enough evidence to support the claim,

That new production method has different standard deviation of length as compared to old method.