Since 1963, when the surgeon general first reported the results of tests linking

Question

Since 1963, when the surgeon general first reported the results of tests linking smoking to several types of physical ailments, cigarette manufacturers have sought to decrease the amount of harmful impurities in their products. One cigarette manufacturer claims that the mean amount of nicotine in cigarettes sold under its brand does not exceed of nicotine. A sample of 16 this manufacturer yields a mean and standard deviation of 16, 4 and 2 mg of nicotine, respectively Do the data provide sufficient evidence to refute the manufacturer's claim? Use a = 10.

Explanation / Answer

Population (N) = 16

Hence we do T test (Since sample size < 30)

Claimed mean (X) = 15

actual mean (U) = 16.4

standard deviation (s) = 2

Alpha = 0.1

Null hypothesis : H 0 : X = U

Alternate hypothsis : Ha : X < 15

we use one tail T test

T = (X-U) / (s/sqrt(n))

= ( 15 - 16.4) / ( 2/ sqrt(16))

= -1.4 * 4 / 2

= -2.8

Hence for df = n-1 = 15 at 0.1 difference,

1.341

Since |caclulated t| > crtical t value

We reject null hypothesis

Hence the cigarette manufacturer claim is correct

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