According to data from the tobacco institute testing

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4)According to data from the Tobacco Institute testing Laboratory, Camel Lights King Size cigarettes contain an average of 1.4 milligrams of nicotine. An advocacy group commissions an independent test to see if the mean nicotine content is higher than the industry laboratory claims. a)Specify the null and alternative hypotheses. b)Suppose that the test statistic is z=2.36. Is this result significant at the 5% level? c)Is the result significant at the 1% level? 5)Assume that SAT mathematics scores of students who attend small liberal arts colleges are normally distributed with N(µ, σ2=8100). We are interested in testing the hypotheses: !!:!=530!!:!<530Given a random sample of size 36 SAT mathematics scores, let the critical region be defined by ={!:!510.77}, where !is the observed mean of the sample. Find the value of the significance level αof this test. 6)Let Xdenote the number of pounds of butterfat produced by a Holstein cow during the 305-day milking period following the birth of a calf. Assume X~ N(µ, σ2=1402We are interested in testing the hypotheses: !!:!=715vs. !!:!<715We have data collected on butterfat weight from 25 cows selected at random. Let the critical region be defined by ={!:!668.94}, where !is the observed mean of the sample. We know the observed sample mean and standard deviation are 667.92 and 154.3616, respectively, a)What is your conclusion about the test? b)Find the value of the significance level αof this test. c)We are also interested in testing whether the claimed variance of σ2=1402isvalidated by our observations. There is belief that the actual variance is larger than 1402. Conduct a test of hypothesis and make a conclusion about this claim. 7)Let !be the mean of a random sample of size nfrom N(µ, σ2=25). To test ). !!:!=20!!:!<20,
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