when people smoke, the nicotine they absorb is converted to cotinine, which can be measured. a sample of 40 smokers has a mean cotinine level of 172.5 with a standard deviation is known to be 119.5, find a 90% confidence interval estimate of the mean cotinine level of all smokers.

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KarpaT KarpaT · Answer 1 · 2022-11-22T04:07:29+01:00

The 90% confidence interval estimate of the mean cotinine level of all smokers is 141.4211 < μ < 203.5789

Given,

Number of smokers; Sample size, n = 40

Mean of the sample, μ = 172.5

Standard deviation, σ = 119.5

We have to find the 90% confidence interval estimate of the mean cotinine level of all smokers.

Here,

The confidence interval is given as;-

x − E < μ < x + E

E is the margin of error.

Margin of error,

E = zα/₂ σ/√n

E = 1.644854 119.5/√40

E = 31.07887

Then,

The confidence interval is;

x − E < μ < x + E

141.4211 < μ < 203.5789

That is,

The 90% confidence interval estimate of the mean cotinine level of all smokers is 141.4211 < μ < 203.5789

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