Question

Independent random samples of 36 and 48 observations are drawn from two quantitative populations, 1 and 2, respectively. The sample data summary is shown here. Sample 1 Sample 2 Sample Size 36 48 Sample Mean 1.28 1.32 Sample Variance 0.0570 0.0520

Do the data present sufficient evidence to indicate that the mean for population 1 is smaller than the mean for population 2? Use one of the two methods of testing presented in this section. (Round your answer to two decimal places.)

z =

Explain your conclusions.

H0 is rejected. There is sufficient evidence to indicate that the mean for population 1 is smaller than the mean for population 2.

H0 is not rejected. There is sufficient evidence to indicate that the mean for population 1 is smaller than the mean for population 2.

H0 is not rejected. There is insufficient evidence to indicate that the mean for population 1 is smaller than the mean for population 2.

H0 is rejected. There is insufficient evidence to indicate that the mean for population 1 is smaller than the mean for population 2.

Answer #1

Claim: The mean for population 1 is smaller than the mean for population 2.

The null and alternative hypothesis is

Level of significance = 0.05

Test statistic is

Critical value = - 1.64 ( using z table)

| Z | < | - 1.64| we fail to reject null hypothesis.

Conclusion: H**0 is not rejected. There is insufficient
evidence to indicate that the mean for population 1 is smaller than
the mean for population 2.**

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 100 observations from a quantitative
population produced a sample mean of 21.5 and a sample standard
deviation of 8.2. Use the p-value approach to determine whether the
population mean is different from 23. Explain your conclusions.
(Use α = 0.05.) State the null and alternative hypotheses. H0: μ =
23 versus Ha: μ < 23 H0: μ = 23 versus Ha: μ > 23 H0: μ = 23
versus Ha: μ ≠ 23 H0: μ <...

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...

The following observations are from two independent random
samples, drawn from normally distributed populations.
Sample 1 [61.43, 78.97, 61.63, 70.48, 66.46, 66.82]
Sample 2 [68.41, 67.18, 65.01, 66.88, 64.06]
Test the null hypothesis H0:σ21=σ22 against the alternative
hypothesis HA:σ21≠σ22.
a) Using the larger sample variance in the numerator, calculate
the F test statistic. Round your response to at least 3 decimal
places.

The following observations are from two independent random
samples, drawn from normally distributed populations.
Sample 1 [59.79, 79.13, 61.82, 55.15, 73.43, 56.37]
Sample 2 [66.05, 66.93, 60.02, 64.24, 60.1]
Test the null hypothesis H0:σ21=σ22 against the alternative
hypothesis HA:σ21≠σ22.
a) Using the larger sample variance in the numerator, calculate
the F test statistic. Round your response to at least 3 decimal
places.

A random sample of n=36 observations is drawn from a population
with a mean equal to 60 and a standard deviation equal to 36.
a. Find the probability that x? is less than 48 ____
b. Find the probability that x? is greater than 63____
c. Find the probability that x? falls between 48 and 78 ____

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

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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