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):*n*1=82,*n*2=84,*x*1=47*x*2=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 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*) is
expressed (-infty, a), an answer of the form (*b*,∞) is
expressed (b, infty), and an answer of the form
(−∞,*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:

**A.** Reject *H*1.

**B.** Do Not Reject *H*0.

**C.** Reject *H*0.

**D.** Do Not Reject *H*1.

Answer #1

The statistical software output for this problem is:

**Two sample proportion summary hypothesis
test:**

p_{1} : proportion of successes for population 1

p_{2} : proportion of successes for population 2

p_{1} - p_{2} : Difference in proportions

H_{0} : p_{1} - p_{2} = 0

H_{A} : p_{1} - p_{2} ≠ 0

**Hypothesis test results:**

Difference |
Count1 |
Total1 |
Count2 |
Total2 |
Sample Diff. |
Std. Err. |
Z-Stat |
P-value |
---|---|---|---|---|---|---|---|---|

p_{1} - p_{2} |
47 | 82 | 47 | 84 | 0.013646922 | 0.076935993 | 0.17738021 | 0.8592 |

Hence,

A) Test statistic = 0.1774

B) Rejection region: (-infty, -2.1084) U (2.1084, infty)

C) p -Value = 0.8592

D) Do not reject Ho

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
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=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=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?...

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...

(1 point)
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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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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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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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Confidence interval =

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Population 1 exercises regularly, and Population 2 does not. The
data from these two samples is given below:
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Population 2: 71, 68, 71, 78, 76, 73, 71, 68
Is there evidence, at an α=0.075, level of significance, to
conclude that there those who exercise regularly have lower resting
heart rates? (Assume that the population variances are equal.)
Carry out an...

(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 =

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students and the other from among UNC students. Both groups are
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