Question

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 test statistic and the rejection region {ybar>k} find the type2 error rate when the true mean of the population is known to be 110. To decrease the type2 error rate we can increase the size of the sample taken. How large would the sample need to be so that alpha=.15 and beta=.05 when using the test statistic ybar, rejection region {ybar>k} and true value of the mean to be 110?

Answer #1

Hypotheses are:

Test is right tailed. The critical value of sample mean for which we will reject the null hypothesis using excel function "=NORMSINV(1-0.15)" is 1.036.

So critical value of sample mean for which we will reject the null hypothesis is

The rejection region is :

The z-score for and is

The type II error is

--------------------------------

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).

Let ?1, ?2, … , ?? denote a random sample from a normal
population distribution with a known value of ?.
(a) For testing the hypotheses ?0: ? = ?0 versus ??: ? > ?0
where ?0 is a fixed number, show that the test with test statistic
?̅ and rejection region ?̅≥ ?0 + 2.33(?⁄√?) has a significance
level 0.01.
(b) Suppose the procedure of part (a) is used to test ?0: ? ≤ ?0
versus ??: ? >...

The observations in the sample are random and independent. The
underlying population distribution is approximately normal. We
consider H0: =15 against Ha: 15. with
=0.05.
Sample statistics: = 16, sx= 0.75, n= 10.
1. For the given data, find the test
statistic
t-test=4.22
t-test=0.42
t-test=0.75
z-test=8.44
z-test=7.5
2.
Decide whether the test statistic is in the rejection region and
whether you should reject or fail to reject the null
hypothesis.
the test statistic is in the rejection region, reject the...

A random sample of 500 of a certain brand of cola was taken to
see whether the mean weight was 16 fluid ounces as indicated on the
container. For the 500 sampled, the mean was found to be 15.9988
with a standard deviation of 0.0985. Does this brand of cola have a
population mean of 16 fluid ounces?
What is the p-value for this hypothesis test?
What is the test statistic for this hypothesis test?
What is the critical value...

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
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...

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 11 observations was taken from a normal
population. The sample mean and standard deviation are xbar= 74.5
and s= 9. Can we infer at the 5% significance level that the
population mean is greater than 70?
I already found the test statistic (1.66) but I’m at a loss for
how to find the p-value.

Let Y_1, … , Y_n be a random sample from a normal distribution
with unknown mu and unknown variance sigma^2. We want to test H_0 :
mu=0 versus H_a : mu !=0. Find the rejection region for the
likelihood ratio test with level alpha.

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 3 minutes ago

asked 29 minutes ago

asked 58 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago