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=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 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

Answer #1

(A)

H0: Null Hypothesis: p1 = p2 ( There is no difference in proportions between first-years and fourth-years)

HA: Alternative Hypothesis: p1 p2 ( There is a difference in proportions between first-years and fourth-years) (Claim)

n1 = 84

1 = 57/84 = 0.6786

n2 = 89

2 = 64/89 = 0.7191

Pooled Proportion is given by:

Test Statistic is given by:

So,

**The value of the standardized test statistic= -
0.581**

(B)

= 0.10

From Table, critical values of Z = 1.64

The rejection region for the standardized test statistic:

**(-infty, - 1.64)U(1.64, infty).**

(C)

By Technology:

**The p-value is 0.5612**

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?...

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=82,n2=84,x1=47x2=47
Is there evidence, at an α=0.035 level of significance,
to conclude that there is a difference in proportions between
first-years and fourth-years? Carry out an appropriate...

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): n1=96, x1=49
Fourth-Years (Pop. 2):n2=88, x2=54
Is there evidence, at an α=0.04 level of significance, to
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1) Independent random samples, each containing 90 observations,
were selected from two populations. The samples from populations 1
and 2 produced 21 and 14 successes, respectively.
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
the other from among UNC students. Both groups are asked if
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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
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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: 71, 67, 61, 62, 67, 70, 68
Population 2: 71, 68, 71, 78, 76, 73, 71, 68
Is there evidence, at an α=0.075, level of significance, to
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Carry out an...

(1 point)
Random samples of resting heart rates are taken from two groups.
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Population 2: 72, 74, 69, 71, 69, 72, 68, 68
Is there evidence, at an α=0.065α=0.065 level of significance,
to conclude that there those who exercise regularly have lower
resting heart rates? (Assume that the population variances are
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