Question

Two random samples are taken, one from among first-year students and the other from among fourth-year students at a public university. Both samples are asked if they favor modifying the student Honor Code. A summary of the sample sizes and number of each group answering yes'' are given below:

First-Years (Pop. 1):Fourth-Years (Pop. 2):n1=86,n2=83,x1=50x2=58First-Years (Pop. 1):n1=86,x1=50Fourth-Years (Pop. 2):n2=83,x2=58

Is there evidence, at an α=0.065α=0.065 level of significance, to conclude that there is a difference in proportions between first-years and fourth-years? Carry out an appropriate hypothesis test, filling in the information requested.

A. The value of the standardized test statistic:

**Note:** For the next part, your answer should use
interval notation. An answer of the form (−∞,a)(−∞,a) is expressed
(-infty, a), an answer of the form (b,∞)(b,∞) is expressed (b,
infty), and an answer of the form (−∞,a)∪(b,∞)(−∞,a)∪(b,∞) is
expressed (-infty, a)U(b, infty).

B. The rejection region for the standardized test statistic:

C. The p-value is

D. Your decision for the hypothesis test :

Answer #1

Ans:

A)

sample proportion 1=50/86=0.5814

sample proportion 2=58/83=0.6988

pooled proportion(50+58)/(86+83)=0.6391

Test statistic:

z=(0.5814-0.6988)/SQRT(0.6391*(1-0.6391)*((1/86)+(1/83)))

z**=-1.589**

B)critical z values=+/-1.845

Reject H0 if z<-1.845 or z>1.845

**(−∞,-1.845)∪(1.845,∞)**

c)p-value=2*P(z<-1.589)=**0.1121**

d)**Fail to reject the null hypothesis.**

There is **not sufficient evidence** to conclude
that there is a difference in proportions between first-years and
fourth-years

Two random samples are taken, one from among first-year students
and the other from among fourth-year students at a public
university. Both samples are asked if they favor modifying the
student Honor Code. A summary of the sample sizes and number of
each group answering yes'' are given below:
First-Years (Pop. 1):Fourth-Years (Pop.
2):n1=93,n2=97,x1=62x2=56First-Years (Pop.
1):n1=93,x1=62Fourth-Years (Pop. 2):n2=97,x2=56
Is there evidence, at an ?=0.07?=0.07 level of significance, to
conclude that there is a difference in proportions between
first-years and fourth-years?...

Two random samples are taken, one from among first-year students
and the other from among fourth-year students at a public
university. Both samples are asked if they favor modifying the
student Honor Code. A summary of the sample sizes and number of
each group answering yes'' are given below:
First-Years (Pop. 1):Fourth-Years (Pop.
2):n1=84,n2=89,x1=57x2=64First-Years (Pop.
1):n1=84,x1=57Fourth-Years (Pop. 2):n2=89,x2=64
Is there evidence, at an α=0.1, level of significance, to
conclude that there is a difference in proportions between
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and the other from among fourth-year students at a public
university. Both samples are asked if they favor modifying the
student Honor Code. A summary of the sample sizes and number of
each group answering yes'' are given below:
First-Years (Pop. 1): n1=96, x1=49
Fourth-Years (Pop. 2):n2=88, x2=54
Is there evidence, at an α=0.04 level of significance, to
conclude that there is a difference in proportions between
first-years and fourth-years?...

Two random samples are taken, one from among first-year students
and the other from among fourth-year students at a public
university. Both samples are asked if they favor modifying the
student Honor Code. A summary of the sample sizes and number of
each group answering yes'' are given below:
First-Years (Pop. 1):Fourth-Years (Pop.
2):n1=82,n2=84,x1=47x2=47
Is there evidence, at an α=0.035 level of significance,
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1) Independent random samples, each containing 90 observations,
were selected from two populations. The samples from populations 1
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Test H0:(p1?p2)=0 against
Ha:(p1?p2)?0. Use
?=0.07.
(a) The test statistic is
(b) The P-value is
(c) The final conclusion is
A. We can reject the null hypothesis that
(p1?p2)=0 and accept that
(p1?p2)?0.
B. There is not sufficient evidence to reject the
null hypothesis that (p1?p2)=0.
2)Two random samples are taken, one from among...

Two random samples are taken, one from among UVA students and
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UVA (Pop. 1):UNC (Pop. 2):n1=88,n2=90,p̂ 1=0.839p̂ 2=0.593UVA
(Pop. 1):n1=88,p^1=0.839UNC (Pop. 2):n2=90,p^2=0.593
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of the population proportions.
Confidence interval =

(1 point)
Two random samples are taken, one from among UVA students and
the other from among UNC students. Both groups are asked if
academics are their top priority. A summary of the sample sizes and
proportions of each group answering yes'' are given below:
UVA (Pop. 1):UNC (Pop. 2):n1=88,n2=90,p̂ 1=0.839p̂ 2=0.593UVA
(Pop. 1):n1=88,p^1=0.839UNC (Pop. 2):n2=90,p^2=0.593
Find a 97.9% confidence interval for the difference p1−p2p1−p2
of the population proportions.
Confidence interval =

(1 point) Two random samples are taken, one from among UVA
students and the other from among UNC students. Both groups are
asked if academics are their top priority. A summary of the sample
sizes and proportions of each group answering yes'' are given
below: UVA (Pop. 1):UNC (Pop. 2):n1=97,n2=95,p^1=0.724p^2=0.628
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Population 1: 72, 62, 64, 64, 65, 72, 68
Population 2: 72, 74, 69, 71, 69, 72, 68, 68
Is there evidence, at an α=0.065α=0.065 level of significance,
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Carry out an...

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