Question

In a test of the hypotheses Ho : μ1 = μ2 versus Ha : μ1 6= μ2 , the observed sample results in a given p-value. Given that the 95% confidence interval for μ1 - μ2 is (-.21.5 , -5.0) based on this give an appropriate p-value for this test.

Answer #1

4.160
Hypotheses: H0 : μ1 =
μ2 vs Ha :
μ1 ≠ μ2. In addition, in
each case for which the results are significant, state which group
(1 or 2) has the larger mean.
(a) 95% confidence interval for μ1 −
μ2 : 0.12 to 0.54
(b) 99% confidence interval for μ1 −
μ2 : −2.1 to 5.4
(c) 90% confidence interval for μ1 −
μ2 : − 10.8 to −3.7

Consider the following hypothesis test.
H0: μ1 − μ2 = 0
Ha: μ1 − μ2 ≠ 0
The following results are from independent samples taken from
two populations assuming the variances are unequal.
Sample 1
Sample 2
n1 = 35
n2 = 40
x1 = 13.6
x2 = 10.1
s1 = 5.7
s2 = 8.2
(a) What is the value of the test statistic? (Use x1
− x2. Round your answer to three decimal
places.)
(b) What is the degrees of...

Consider the following hypothesis test.
H0: μ1 − μ2 = 0
Ha: μ1 − μ2 ≠ 0
The following results are from independent samples taken from
two populations.
Sample 1
Sample 2
n1 = 35
n2 = 40
x1 = 13.6
x2 = 10.1
s1 = 5.9
s2 = 8.5
(a)
What is the value of the test statistic? (Use
x1 − x2.
Round your answer to three decimal places.)
(b)
What is the degrees of freedom for the t...

The null and alternate hypotheses are:
H0 : μ1 =
μ2
H1 : μ1 ≠
μ2
A random sample of 9 observations from one population revealed a
sample mean of 24 and a sample standard deviation of 3.7. A random
sample of 6 observations from another population revealed a sample
mean of 28 and a sample standard deviation of 4.6.
At the 0.01 significance level, is there a difference between
the population means?
a. State the decision rule.
b.Compute the...

In a test of the hypothesis Ho: μ = 50
versus Ha: μ ≠ 50,
with a sample of n = 100 has a Sample Mean = 49.4 and Sample
Standard Deviation, S = 4.1.
(a) Find the p-value for the test. (b)
Interpret the
p-value for the test, using
an α =
0.10.

Use the t-distribution and the given sample results to
complete the test of the given hypotheses. Assume the results come
from random samples, and if the sample sizes are small, assume the
underlying distributions are relatively normal.
Test H0 : μ1=μ2 vs Ha : μ1≠μ2 using the sample results x¯1=15.3,
s1=11.6 with n1=100 and x¯2=18.4, s2=14.3 with n2=80.
(a) Give the test statistic and the p-value.
Round your answer for the test statistic to two decimal places and
your answer...

Use the t-distribution and the given sample results to
complete the test of the given hypotheses. Assume the results come
from random samples, and if the sample sizes are small, assume the
underlying distributions are relatively normal.
Test H0 : μ1=μ2 vs Ha : μ1≠μ2 using the sample results x¯1=15.3,
s1=11.6 with n1=100 and x¯2=18.4, s2=14.3 with n2=80.
(a) Give the test statistic and the p-value.
Round your answer for the test statistic to two decimal places and
your answer...

Use the t-distribution to find a confidence interval
for a difference in means μ1-μ2 given the relevant sample results.
Give the best estimate for μ1-μ2, the margin of error, and the
confidence interval. Assume the results come from random samples
from populations that are approximately normally distributed.
A 90% confidence interval for μ1-μ2 using the sample results
x¯1=81.1, s1=10.3, n1=35 and x¯2=67.1, s2=7.9, n2=20
Enter the exact answer for the best estimate and round your answers
for the margin of...

A confidence interval for a sample is given, followed by several
hypotheses to test using that sample. In each case, use the
confidence interval to give a conclusion of the test (if possible)
and also state the significance level you are using.
A 99% confidence interval for
μ :120 to 168
a) Ho: μ = 104 vs Ha: μ ≠
104
Conclusion _____ Ho
(reject or do not reject)
Significance level: _______
(10%, 5%, 95%, 1%, 90% or 99%)...

Suppose μ1 and μ2 are true mean stopping distances at 50 mph for
cars of a certain type equipped with two different types of braking
systems. Use the two-sample t-test at significance level 0.01 to
test H0: μ1 − μ2 = −10 versus Ha: μ1 − μ2 < −10 for the
following data: m = 8, x = 114.4, s1 = 5.01, n = 8, y = 129.2, and
s2 = 5.32.
Calculate the test statistic and determine the P-value....

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