Conduct a test at the alphaαequals=0.100.10 level of significanc

Conduct a test at the alphaαequals=0.100.10 level of significance by determining ​(a) the null and alternative​ hypotheses, ​(b) the test​ statistic, and​ (c) the​ P-value. Assume the samples were obtained independently from a large population using simple random sampling. Test whether p 1 greater than p 2p1>p2. The sample data are x 1 equals 120×1=120​, n 1 equals 253n1=253​, x 2 equals 132×2=132​, and n 2 equals 319n2=319. Construct a confidence interval for p 1 minus p 2p1−p2 at the given level of confidence. x 1 equalsx1=384​, n 1 equalsn1=524​, x 2 equalsx2=414​, n 2 equalsn2=558​, 90​% confidence In a clinical trial of a​ vaccine, 8,000 children were randomly divided into two groups. The subjects in group 1​ (the experimental​ group) were given the vaccine while the subjects in group 2​ (the control​ group) were given a placebo. Of the 4,000 children in the experimental​ group, 75 developed the disease. Of the 4,000 children in the control​ group, 106 developed the disease. Determine whether the proportion of subjects in the experimental group who contracted the disease is less than the proportion of subjects in the control group who contracted the disease at the alphaαequals=0.10 level of significance. A researcher wants to show the mean from population 1 is less than the mean from population 2 in​ matched-pairs data. If the observations from sample 1 are  Xi and the observations from sample 2 are  Yi​,  and  diequals=Ximinus−Yi​,  then the null hypothesis is  H0​:  muμdequals=0  and the alternative hypothesis is  H1​:  muμd  ​___ 0.

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