Answer to Question #244939 in Statistics and Probability for boo

Question

A manufacturer of tobacco products plans to market a new brand of cigarette. The regulatory
commission needs to know the mean tar content for the new brand. Analysis of a random sample
of 25 of the new brand of cigarettes gives a mean tar content of 10.98 milligrams with a standard
deviation of 0.604 milligram. Construct a 95% confidence interval for the mean tar content of
the new brand.

Answer 1

Population standard deviation is unknown , we will use t test

Degrees of freedom $=n-1=25-1=24$

Critical value=

$t_{α/2, df} = t_{0.05/2.24} = t_{0.025, 24} = ±2.0639$

95% confidence interval is given by

$\bar{x} ± t_{α/2, df} \times \frac{s}{\sqrt{n}} \\ = (10.98 -2.0639 \times \frac{0.604}{\sqrt{25}} < \mu < 10.98 + 2.0639 \times \frac{0.604}{\sqrt{25}}) \\ = (10.98 -0.24932 < \mu < 10.98 + 0.24932) \\ = (10.73068 < \mu < 11.22932)$