Question

Independent random samples of

n_{1} = 600

and

n_{2} = 440

observations were selected from binomial populations 1 and 2, and

x_{1} = 334

and

x_{2} = 378

successes were observed.

(a) Find a 90% confidence interval for the difference
(*p*_{1} − *p*_{2}) in the two
population proportions. (Round your answers to three decimal
places.)

to

(b) What assumptions must you make for the confidence interval to
be valid? (Select all that apply.)

independent samples

random samples

*n*q̂ > 5 for samples from both populations

n_{1} + n_{2} > 1,000

*n*p̂ > 5 for samples from both populations

symmetrical distributions for both populations

Answer #1

Independent random samples of
n1 = 700
and
n2 = 590
observations were selected from binomial populations 1 and 2,
and
x1 = 337
and
x2 = 375
successes were observed.
(a) Find a 90% confidence interval for the difference
(p1 − p2) in the two
population proportions. (Round your answers to three decimal
places.)

Independent random samples of
n1 = 900 and n2 = 900
observations were selected from binomial populations 1 and 2,
and
x1 = 120
and
x2 = 150
successes were observed.
(a)
What is the best point estimator for the difference
(p1 − p2)
in the two binomial proportions?
p̂1 − p̂2
n1 −
n2
p1 − p2
x1 − x2
(b)
Calculate the approximate standard error for the statistic used
in part (a). (Round your answer to three decimal...

Independent random samples of
n1 = 170
and
n2 = 170
observations were randomly selected from binomial populations 1
and 2, respectively. Sample 1 had 96 successes, and sample 2 had
103 successes.
You wish to perform a hypothesis test to determine if there is a
difference in the sample proportions
p1
and
p2.
(a)
State the null and alternative hypotheses.
H0:
(p1 − p2)
< 0 versus Ha:
(p1 − p2)
> 0
H0:
(p1 − p2)
= 0...

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 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) 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...

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

The numbers of successes and the sample sizes for independent
simple random samples from two populations are x1=15, n1=30, x2=59,
n2=70. Use the two-proportions plus-four z-interval procedure to
find an 80% confidence interval for the difference between the two
populations proportions. What is the 80% plus-four confidence
interval?

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.

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