Question

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 *H*0:(*p*1?*p*2)=0 against
*H**a*:(*p*1?*p*2)?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
(*p*1?*p*2)=0 and accept that
(*p*1?*p*2)?0.

**B.** There is not sufficient evidence to reject the
null hypothesis that (*p*1?*p*2)=0.

2)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=84,*n*2=88,*x*1=43*x*2=38

Is there evidence, at an *?*=0.08 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.** Do Not Reject *H*0.

**B.** Reject *H*1.

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

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

Answer #1

Solution1:

H0:(p1?p2)=0

Ha:(p1?p2)?0

alpha=0.07

(a) The test statistic i

Z=p1^-p2^/sqrt(p1^(1-p1^)/n1+p2^(1-p2^)n2)

p1^=x1/n1=21/90=0.2333333

p2^=x2/n2=14/90=0.1555556

z=0.2333333-0.1555556/sqrt(0.2333333(1-0.2333333)/90+0.1555556(1-0.1555556)/90

z=1.318

Solutionb:

p value=0.1874

Solutionc:

p value=0.1874

p>0.07

Do not Reject Null Hypothesis.

Accept Null Hypothesis.

(c) The final conclusion is

There is not sufficient evidence to reject the null hypothesis that (p1?p2)=0.

Independent random samples, each containing 90 observations,
were selected from two populations. The samples from populations 1
and 2 produced 73 and 64 successes, respectively.
Test H0:(p1−p2)=0 against Ha:(p1−p2)≠0. Use α=0.09
The P-value is
The final conclusion is
A. There is not sufficient evidence to reject the
null hypothesis that (p1−p2)=0
B. We can reject the null hypothesis that
(p1−p2)=0 and accept that (p1−p2)≠0

Independent random samples, each containing 80 observations,
were selected from two populations. The samples from populations 1
and 2 produced 16 and 10 successes, respectively.
Test H0:(p1−p2)=0 against Ha:(p1−p2)≠0. Use α=0.1
(a) The test statistic is
(b) The P-value is
(c) The final conclusion is
A. There is not sufficient evidence to reject the
null hypothesis that (p1−p2)=0
B. We can reject the null hypothesis that
(p1−p2)=0 and accept that (p1−p2)≠0

1 point) Independent random samples, each containing 80
observations, were selected from two populations. The samples from
populations 1 and 2 produced 30 and 23 successes,
respectively.
Test H0:(p1−p2)=0H0:(p1−p2)=0 against Ha:(p1−p2)≠0Ha:(p1−p2)≠0. Use
α=0.01α=0.01.
(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(p1−p2)=0 and accept that (p1−p2)≠0(p1−p2)≠0.
B. There is not sufficient evidence to reject the
null hypothesis that (p1−p2)=0(p1−p2)=0.

Independent random samples, each containing 70 observations,
were selected from two populations. The samples from populations 1
and 2 produced 42 and 35 successes, respectively. Test H0:(p1−p2)=0
H 0 : ( p 1 − p 2 ) = 0 against Ha:(p1−p2)≠0 H a : ( p 1 − p 2 ) ≠
0 . Use α=0.06 α = 0.06 . (a) The test statistic is (b) The P-value
is (c) The final conclusion is A. There is not sufficient evidence...

Independent random samples, each containing 90 observations,
were selected from two populations. The samples from populations 1
and 2 produced 44 and 35 successes, respectively.
Test H0:(p1?p2)=0H0:(p1?p2)=0 against
Ha:(p1?p2)>0Ha:(p1?p2)>0. Use ?=0.02?=0.02
(a) The test statistic is:
(b) The P-value is:

Independent random samples, each containing 70 observations,
were selected from two populations. The samples from populations 1
and 2 produced 33 and 23 successes, respectively. Test H 0 :( p 1 −
p 2 )=0 H0:(p1−p2)=0 against H a :( p 1 − p 2 )≠0 Ha:(p1−p2)≠0 .
Use α=0.01 α=0.01 . (a) The test statistic is
(b) The P-value is
(c) The final conclusion is
A. We can reject the null hypothesis that ( p 1 − p 2...

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?...

Independent random samples, each containing 50 observations,
were selected from two populations. The samples from populations 1
and 2 produced 31 and 25 successes, respectively. Test H0:(p1−p2)=0
against Ha:(p1−p2)≠0. Use α=0.05.
(a) The test statistic is
(b) The P-value is

(1 point) Independent random samples, each containing 60
observations, were selected from two populations. The samples from
populations 1 and 2 produced 34 and 29 successes, respectively.
Test H0:(p1−p2)=0 H 0 : ( p 1 − p 2 ) = 0 against Ha:(p1−p2)≠0 H a
: ( p 1 − p 2 ) ≠ 0 . Use α=0.07 α = 0.07 .
(a) The test statistic is
(b) The P-value is

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