Quarters are currently minted with weights normally distributed and sample of 26
ID: 2949212 • Letter: Q
Question
Quarters are currently minted with weights normally distributed and sample of 26 quarters is obtained from those manufactured having a standard deviation of 0.069 New equipment is being tested in an attempt to improve quality by reducing vanation A simple random with the new equipment, and this sample has a standard deviation of 0 049 Use a 0,025 significance level to test the claim that quart equipment appear to be effective in reducing the variation of weights? new ers manufactured wit the new equipment have weights with a standard deviation less than 0 069. Does the nea a) Wnite the claim mathemadically and identy Ho and a t OD, Ho: as0009: Hro»O009 (Claim)Explanation / Answer
a) Ans C Null Hypothesis states the status quo and whatever claim needs to be tested should be included in Alternate Hypothesis. Since the claim is to test that the quarters manufactured with the new equipment have weights with standard deviation less than 0.069 hence :
H0 >= 0.069 , Ha < 0.069 (Claim)
b) Answer A Since this is a left tailed test, hence A is the answer
c) X2 = (Observed - Expected)2/Expected
= (0.049-0.069)2/(0.069)
= 0.0058 = 0.006 (Round to three decimal places)
d) Reject H0 if X2 >= critical value
Critical value with 25 Degrees of freedom (26-1) and significance level = 0.025 is 13.12
Since 0.006 < 13.12, hence Null Hypothesis cannot be rejected
Answer Fail to Reject
e) Answer D Since the null hypothesis is not rejected, the new equipment doesn't appear to be more effective