Question

In order to compare the means of two populations, independent random samples of 282 observations are selected from each population, with the following results:

Sample 1 | Sample 2 |

x¯1=3 | x¯2=4 |

s1=110 | s2=200 |

(a) Use a 97 % confidence interval to
estimate the difference between the population means
(?1−?2)(μ1−μ2).

_____ ≤(μ1−μ2)≤ ______

(b) Test the null hypothesis: H0:(μ1−μ2)=0
versus the alternative hypothesis: Ha:(μ1−μ2)≠0. Using ?=0.03, give
the following:

(i) the test statistic z=

(ii) the positive critical z score

(iii) the negative critical z score

The final conclusion is

We can reject the null hypothesis (μ1−μ2)=0 in favor of the
alternative (μ1−μ2)≠0.

There is not sufficient evidence to reject the null hypothesis
(μ1−μ2)=0.

(c) Test the null hypothesis: H0:(μ1−μ2)=23 versus the alternative hypothesis: Ha:(μ1−μ2)≠23. Using ?=0.03, give the following:

(i) the test statistic z=

(ii) the positive critical z score

(iii) the negative critical z score

The final conclusion is

We can reject the null hypothesis (μ1−μ2)=23 in favor of the
alternative (μ1−μ2)≠23.

There is not sufficient evidence to reject the null hypothesis
(μ1−μ2)=23.

Answer #1

In order to compare
the means of two normal populations, independent random samples are
taken of sizes n1 = 400 and n2 = 400. The
results from the sample data yield:
Sample 1
Sample 2
sample mean = 5275
sample mean = 5240
s1 = 150
s2 = 200
To test the null
hypothesis H0: µ1 - µ2 = 0 versus
the alternative hypothesis Ha: µ1 -
µ2 > 0 at the 0.01 level of significance, the most
accurate statement...

Independent random samples of 42 and 36 observations are drawn
from two quantitative populations, 1 and 2, respectively. The
sample data summary is shown here.
Sample 1
Sample 2
Sample Size
42
36
Sample Mean
1.34
1.29
Sample Variance
0.0510
0.0560
Do the data present sufficient evidence to indicate that the
mean for population 1 is larger than the mean for population 2?
Perform the hypothesis test for H0:
(μ1 − μ2) = 0 versus
Ha: (μ1 −
μ2) >...

A random sample of 140 observations is selected from a binomial
population with unknown probability of success p. The computed
value of p^ is 0.71.
(1) Test H0:p≤0.65 against Ha:p>0.65. Use α=0.01. test
statistic z= critical z score The decision is A. There is
sufficient evidence to reject the null hypothesis.
B. There is not sufficient evidence to reject the null
hypothesis.
(2) Test H0:p≥0.5 against Ha:p<0.5. Use α=0.01. test
statistic z= critical z score The decision is A. There...

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 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

Two independent samples have been selected, 55 observations from
population 1 and 72observations from population 2. The sample means
have been calculated to be x¯1=10.7 and x¯2=8.3. From previous
experience with these populations, it is known that the variances
are σ21=30 and σ22=23.
(a) Determine the rejection region for the test of
H0:(μ1−μ2)=2.77
H1:(μ1−μ2)>2.77
using α=0.04.
z > __________
(b) Compute the test statistic.
z =
The final conclusion is
A. We can reject H0.
B. There is not sufficient...

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.

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 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 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...

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