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Karolina [17]
3 years ago
9

A researcher studied the radioactivity of asbestos. She sampled 81 boards of asbestos, and found a sample mean of 193.2 bips, an

d a sample standard deviation of 49.5 bips. (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?
Mathematics
1 answer:
Ksivusya [100]3 years ago
3 0

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,

\bar{x}-z\times \frac{\sigma}{\sqrt{n}}

We have given,            

The sample mean \bar{x}=193.2 bips

s is the standard deviation \sigma=49.5 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,

193.2-1.88\times \frac{49.5}{\sqrt{81}}

193.2-1.88\times 5.5

193.2-10.34

182.86

Confidence interval is (182.86,203.54).    

b) (i) According the interval 182.86

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.

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