An experiment is performed to determine whether the average nicotine content of one kind of cigarette exceeds that of another kind by 0.20 milligram. If =50 cigarettes of the first kind had an average nicotine content of =2.61 milligrams with a standard deviation of =0.12 milligram, whereas =40 cigarettes of the other kind had an average nicotine content of = 2.38 milligrams with a standard deviation of =0.14 milligram, test the null hypotheses - = 0.20 against the alternative hypotheses - ¹ 0.20 at the 0.05 level of significance.
We have independent random samples from two normal populations having mean and known variances. We want to teat the null hypothesis , where δ is a given constant, against of the alternative . The appropriate test statistic for this test is
Test concerning differences between means
When we deal with independent random sample from populations with unknown variances which may not even be normal, the test can still be used with substituted for and substituted for so long as both samples are large enough for the central limit theorem to be invoked.
Reject if z≥1.96
Since z=1.08 < 1.96, we cannot reject the null hypothesis.
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