statistics questions

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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 120x1=120​,
n 1 equals 253n1=253​,
x 2 equals 132x2=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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