Question

Two different simple random samples are drawn from two different populations. The first sample consists of 20 people with 10 having a common attribute. The second sample consists of 2200 people with 1595 of them having the same common attribute. Compare the results from a hypothesis test of p1 = p2 (with a 0.01 significance level) and a 99% confidence interval estimate of p1 - p2.

1. Identify the test statistic ____ (round to 2 decimal places)

2. Identify the critical values ____ (round to 3 decimal places)

3. The test statistic is ______ the critical region, so _______ the null hypothesis. There is _______ evidence to conclude that p1 does not equal p2.

4. The 99% confidence interval is _____ < (p1 - p2) < ____

What is the conclusion based on the confidence interval?

5. Since 0 is _____ in the interval, it indicates to _____ the null hypothesis

How do the results from the hypothesis test and the confidence interval compare?

6. The results are _____, since the hypothesis test suggests that p1 ____ p2, and the confidence interval suggests that p1 ______ p2.

Answer #1

Two different simple random samples are drawn from two different
populations. The first sample consists of 20 people with 11 having
a common attribute. The second sample consists of 1800 people with
1283 of them having the same common attribute. Compare the results
from a hypothesis test of p1 =p2 (with a
0.05 significance level) and a 95% confidence interval estimate
of p1 - p2
What are the null and alternative hypotheses for the
hypothesis test?
Identify the test statistic.(Round...

Two different simple random samples are drawn from two different
populations. The first sample consists of 30 people with 15 having
a common attribute. The second sample consists of 2100 people with
1477 of them having the same common attribute. Compare the results
from a hypothesis test of p1 =p2 (with a 0.05 significance level)
and a 95% confidence interval estimate of p1 - p2 What are the
null and alternative hypotheses for the hypothesis test. Identify
the test statistic.(Round...

Two different simple random samples are drawn from two different
populations. The first sample consists of 30 people with 15 having
a common attribute. The second sample consists of 1900 people with
1379 of them having the same common attribute. Compare the results
from a hypothesis test of p1=p2 (with a 0.01 significance level)
and a 99% confidence interval estimate of p1−p2.
Find hypothesis, test statistic, critical value, p value, and
95% CL.

Two different simple random samples are drawn from two different
populations. The first sample consists of 30 people with 14 having
a common attribute. The second sample consists of 1800 people with
1294 of them having the same common attribute. Compare the results
from a hypothesis test of p1= p2 (with a 0.05 significance level)
and a 95% confidence interval estimate of p1−p2.
Identify hypothesis, t statistic, critical value, p value

Two different simple random samples are drawn from two different
populations. The first sample consists of
2020
people with
1111
having a common attribute. The second sample consists of
22002200
people with
15801580
of them having the same common attribute. Compare the results
from a hypothesis test of
p 1p1equals=p 2p2
(with a
0.050.05
significancelevel) and a
9595%
confidence interval estimate of
p 1p1minus−p 2p2.

Independent random samples, each containing 60 observations,
were selected from two populations. The samples from populations 1
and 2 produced 42 and 30 successes, respectively.
Test H0:(p1−p2)=0 against Ha:(p1−p2)≠0. Use α=0.09
(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 500 observations,
were selected from two binomial populations. The samples from
populations 1 and 2 produced 388 and 188 successes,
respectively.
(a) Test H0:(p1−p2)=0 against Ha:(p1−p2)≠0. Use α=0.04
test statistic =
rejection region |z|>
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 support
that (p1−p2)≠0.
(b) Test H0:(p1−p2)≤0 against Ha:(p1−p2)>0. Use α=0.03
test statistic =
rejection...

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

Independent random samples, each containing 60 observations,
were selected from two populations. The samples from populations 1
and 2 produced 26 and 15 successes, respectively. Test H0:(p1−p2)=0
against Ha:(p1−p2)>0 Use α=0.08
(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

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...

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