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

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...

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...

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...

A random sample of 37 second graders who participated in sports
had manual dexterity scores with mean 32.29 and standard
deviation
4.14.
An independent sample of 37 second graders who did not
participate in sports had manual dexterity scores with mean 31.88
and standard deviation
4.86.
(a)
Test to see whether sufficient evidence exists to indicate that
second graders who participate in sports have a higher mean
dexterity score. Use
α = 0.05.
State the null and alternative hypotheses. (Us...

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