Alcohol content in beer is believed to follow a normal distribution. A chemist t

Question

Alcohol content in beer is believed to follow a normal distribution. A chemist takes a sample from 9 bottles of beer and measures the alcohol content, finding a sample mean of 7.5% and a sample standard deviation of 1%. The chemist wishes to compute a 90% confidence interval for the mean. However, the chemist mistakenly treats the sample standard deviation as if it were the population standard deviation. What is the confidence interval constructed by the chemist?

A) (6.647, 8.153) B) (6.952, 8.048) C) (6.880, 8.120) D) (7.073, 7.927) E) (7.034, 7.966)

Suppose the chemist in the previous question realises he has made a mistake. If he correct his mistake and recalculates the confidence interval using the same sample, how will the new confidence interval compare to the previous one?

A) The new interval will be the same width as the previous one and will be shifted to the left to account for small sample bias.

B) The new interval will be wider than the previous one and will be centered around the same point estimate.

C) The new interval will be narrower than the previous one and will be centered around the same point estimate.

D) Thenewintervalwillbenarrowerthanthepreviousoneandwillbeshiftedtothelefttoaccount for small sample bias.

E) This cannot be determined from the data given.

Explanation / Answer

Confiedance Interval is calculated by (X_-z*std.deviation, X_+z*std deviation)

We have Sample Mean =X_, z= Z score for confieance interval of 90% and Standard Deviation given

X_=7.5%, Std dev=1%

for 90% confiedance interval we have z value equals to 1.64 therefore

(7.5%-(1.64*1%)/3,7.5%+(1.64*1%)/3) hence Calculated Confiedance interval is (6.953%,8.0466%)

Option B is correct answer

Ans 2)

Now if he realises that he has mad mistake then new confiedance interval would be more wide

New Confiedance Interval is ((7.5%-(1.64*0.01)),(7.5%+(1.64*0.01))=(5.86,9.14)

Hence option B is correct asnwer as still mean is same

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