Question

- A sample of size 10 is taken from the first population: Sample mean of 101.2 and sample variance of 18.1
- A sample of size 14 is taken from the second population: Sample mean of 98.7 and sample variance of 9.7

a)In order to decide whether pooling is appropriate or not, performing a test at α = 0.2 level of significance : Find the rejection region.

b)In order to decide whether pooling is appropriate or not, performing a test at α = 0.2 level of significance : Find the observed value of the test statistic.

c)If a significance level, not necessarily equal to the choice
of questions a and c, is used when the decision on pooling is made
and pooling is found to be appropriate: We wish to compare the
means of two populations at α = 0.1 level, testing: **Ho: μ1
= μ2 (against H1: μ1** **>**
**μ2)**. Find the rejection region.

Need an answer for c is important.

Answer #1

A sample of size 10 is taken from the first population: Sample
mean of 101.2 and sample variance of 18.1
A sample of size 14 is taken from the second population: Sample
mean of 98.7 and sample variance of 9.7
a)In order to decide whether pooling is appropriate or not,
performing a test at α = 0.2 level of significance : Find the
rejection region.
b)In order to decide whether pooling is appropriate or not,
performing a test at α...

A sample of size 10 is taken from the first population: Sample
mean of 101.2 and sample variance of 18.1
A sample of size 14 is taken from the second population: Sample
mean of 98.7 and sample variance of 9.7
1)In order to decide whether pooling is appropriate or not,
performing a test at α = 0.2 level of significance : Find the
rejection region.
2)In order to decide whether pooling is appropriate or not,
performing a test at α...

Consider a sample of size 22 taken from a normal population. The
sample mean is 2.625 and the sample standard deviation is 0.13. We
test Ho: μ = 2.7 versus H1: μ ≠ 2.7 at the α
= 0.05 level. The rejection region and our decision are
Select one:
a. t < - 1.721 & t > 1.721; REJECT Ho
b. t < - 2.080 & t > 2.080; REJECT Ho
c. t < - 1.717 & t > 1.717; DO NOT...

Using a random sample of size 77 from a normal population with
variance of 1 but unknown mean, we wish to test the null hypothesis
that H0: μ ≥ 1 against the alternative that Ha: μ <1.
Choose a test statistic.
Identify a non-crappy rejection region such that size of the
test (α) is 5%. If π(-1,000) ≈ 0, then the rejection region is
crappy.
Find π(0).

Using the following information:
For the first population: sample size of 30 taken from the
population, sample mean 1.32 , population variance 0.9734.
For the second population : sample size of 30 taken from the
population, sample mean 1.04,
population variance 0.7291.
Find a 90% confidence interval for the difference between the
two population means.

A sample of size 12, taken from a normally distributed
population has a sample mean of 85.56 and a sample standard
deviation of 9.70. Suppose that we have adopted the null hypothesis
that the actual population mean is equal to 89, that is, H0 is that
μ = 89 and we want to test the alternative hypothesis, H1, that μ ≠
89, with level of significance α = 0.1.
a) What type of test would be appropriate in this situation?...

suppose a random sample of 25 is taken from a population that
follows a normal distribution with unknown mean and a known
variance of 144. Provide the null and alternative hypothesis
necessary to determine if there is evidence that the mean of the
population is greater than 100. Using the sample mean ybar as the
test statistic and a rejection region of the form {ybar>k} find
the value of k so that alpha=.15 Using the sample mean ybar as the...

A random sample of 49 measurements from one population had a
sample mean of 16, with sample standard deviation 3. An independent
random sample of 64 measurements from a second population had a
sample mean of 18, with sample standard deviation 4. Test the claim
that the population means are different. Use level of significance
0.01.
(a) What distribution does the sample test statistic follow?
Explain.
The Student's t. We assume that both population
distributions are approximately normal with known...

A random sample of size n1 = 25, taken from a normal
population with a standard deviation σ1 = 5.2, has a
sample mean = 85. A second random sample of size n2 =
36, taken from a different normal population with a standard
deviation σ2 = 3.4, has a sample mean = 83. Test the
claim that both means are equal at a 5% significance level. Find
P-value.

A random sample of
n1 = 49
measurements from a population with population standard
deviation
σ1 = 5
had a sample mean of
x1 = 11.
An independent random sample of
n2 = 64
measurements from a second population with population standard
deviation
σ2 = 6
had a sample mean of
x2 = 14.
Test the claim that the population means are different. Use
level of significance 0.01.
(a) Check Requirements: What distribution does the sample test
statistic follow? Explain....

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