Answer:
a) Confidence interval is (182.86,203.54).
b) (i) Yes, 200 bips is a true mean as it lie in the interval.
(ii) No, 210 bips is not a true mean as it doesn't lie in the interval.
Step-by-step explanation:
Given : A researcher studied the radioactivity of asbestos. She sampled 81 boards of asbestos, and found a sample mean of 193.2 bips, and a sample standard deviation of 49.5 bips.
To find : (a) Obtain the 94% confidence interval for the mean radioactivity. (b) (i) According the interval that you got, is 200 bips a plausible value for the true mean? (ii) What about 210 bips?
Solution :
a) The confidence interval formula is given by,
We have given,
The sample mean bips
s is the standard deviation bips
n is the number of sample n=81
z is the score value, at 94% z=1.88
Substitute all the values in the formula,
Confidence interval is (182.86,203.54).
b) (i) According the interval
200 bips a plausible value for the true mean as it lies in the interval.
(ii) 210 bips not lie in the confidence interval so it is not a true mean.