Answer:
Yes, the new equipment appear to be effective in reducing the variation of weights.
Step-by-step explanation:
We are given that Quarters are currently minted with weights normally distributed and having a standard deviation of 0.065.
A simple random sample of 25 quarters is obtained from those manufactured with the new equipment, and this sample has a standard deviation of 0.047.
Let = <u><em>standard deviation of weights of new equipment.</em></u>
SO, Null Hypothesis, :
0.065 {means that the new equipment have weights with a standard deviation more than or equal to 0.065}
Alternate Hypothesis, :
< 0.065 {means that the new equipment have weights with a standard deviation less than 0.065}
The test statistics that would be used here <u>One-sample chi-square</u> test statistics;
T.S. = ~
where, s = sample standard deviation = 0.047
n = sample of quarters = 25
So, <u><em>the test statistics</em></u> = ~
= 12.55
The value of chi-square test statistics is 12.55.
Now, at 0.05 significance level the chi-square table gives critical value of 13.85 at 24 degree of freedom for left-tailed test.
Since our test statistic is less than the critical value of chi-square as 12.55 < 13.85, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which <u><em>we reject our null hypothesis</em></u>.
Therefore, we conclude that the new equipment have weights with a standard deviation less than 0.065.