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Answer:
99% confidence interval for the given specimen is [3.4125 , 3.4155].
Step-by-step explanation:
We are given that a laboratory scale is known to have a standard deviation (sigma) or 0.001 g in repeated weighing. Scale readings in repeated weighing are Normally distributed with mean equal to the true weight of the specimen.
Three weighing of a specimen on this scale give 3.412, 3.416, and 3.414 g.
Firstly, the pivotal quantity for 99% confidence interval for the true mean specimen is given by;
P.Q. = ~ N(0,1)
where, = sample mean weighing of specimen =
= 3.414 g
= population standard deviation = 0.001 g
n = sample of specimen = 3
= population mean
<em>Here for constructing 99% confidence interval we have used z statistics because we know about population standard deviation (sigma).</em>
So, 99% confidence interval for the population mean, is ;
P(-2.5758 < N(0,1) < 2.5758) = 0.99 {As the critical value of z at 0.5% level
of significance are -2.5758 & 2.5758}
P(-2.5758 < < 2.5758) = 0.99
P( <
<
) = 0.99
P( <
<
) = 0.99
<u>99% confidence interval for</u> = [
,
]
= [ ,
]
= [3.4125 , 3.4155]
Therefore, 99% confidence interval for this specimen is [3.4125 , 3.4155].