A 1-kg check weight is weighed 225 times on a very accurate scale. The average w
ID: 3224653 • Letter: A
Question
A 1-kg check weight is weighed 225 times on a very accurate scale. The average weighing was 999.937g, and the sd of the weighing was 0.45g. Assume the Gauss Model.
3. True of false (referring to the confidence interval-which is a range):
(a) About 95% of the 225 weighings were in this range.
(b) There is about a 95% chance that a 226th measurement will fall in this range.
(c) If 225 more weighings were done, there is a 95% chance that their average would fall in this range.
(d) If 900 weighings had been done to find a confidence interval, that interval would most likely have been smaller than this result.
(e) There is no point in finding a 95% confidence interval for the average of the 225 weighings.
Explanation / Answer
Q.3 T and F
(a)About 95% of the 225 weighings were in this range. No
The given confidence interval is the Confidence interval of mean value of 225 measurement of 1- kg check weight, it is not the confidecne interval of sampling so the statement is untrue.
(b) There is about a 95% chance that a 226th measurement will fall in this range. No
The confidence interval here is the confidence interval of Mean weight of 1-kg check weight not of sample values. So, it is untrue that 226th measurement will fall in this range has 95% chance.
(c) If 225 more weighing were done, there is a 95% chance that their average would fall in this range. Yes
This is same as the above confidence interval , which was the 95% CI of sample mean of 225 observations. So a new sample will also have same 95% chance tat their average would fall in this range.
(d) If 900 weighing had been done to find a confidence interval, that interval would most likely have been smaller than this result. YES
It is because, confidence interval are inversely proportional to sample size., so the statement is true that interval would most likely to be smaller than this result.
(e) There is no point in finding a 95% confidence interval for the average of the 225 weighing. NO.
There is absolutely valid reason to find 95% confidence interval to check the authenticity of the given 1- kg check weight that it is the original one or shows less weight than specification.
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