Question

An alternative hypothesis in a one-sample Z test could be represented as:

H_{1}: *X* > *µ*

H_{0}: *X* > *µ*

H_{1}: *X* = *µ*

H_{0}: *X* < *µ*

Answer #1

Here the answer is,

In Testing of Hypothesis, The Null hypothesis is denoted by i.e. and Alternative Hypothesis is denoted by .

In one sample z test ,The alternative hypothesis ( ) is one sided and left tail test then the alternative hypothesis is denoted by

AND the alternative hypothesis ( ) is one sided and right tailed test then the alternative hypothesis is denoted by

and the alternative hypothesis ( ) is two tailed alternative then the alternative hypothesis is denoted by

1. In order to test H0: µ=40 versus H1: µ > 40, a random
sample of size n=25 is obtained from a population that is known to
be normally distributed with sigma=6.
. The researcher decides to test this hypothesis at the α =0.1
level of significance, determine the critical value.
b. The sample mean is determined to be x-bar=42.3, compute the
test statistic z=???
c. Draw a normal curve that depicts the critical region and
declare if the null...

. Consider the following hypothesis test: H0 : µ ≥ 20 H1 : µ
< 20 A sample of 40 observations has a sample mean of 19.4. The
population standard deviation is known to equal 2. (a) Test this
hypothesis using the critical value approach, with significance
level α = 0.01. (b) Suppose we repeat the test with a new
significance level α ∗ > 0.01. For each of the following
quantities, comment on whether it will change, and if...

Suppose that we wish to test H0: µ = 20 versus
H1: µ ≠ 20, where σ is known to equal 7. Also, suppose
that a sample of n = 49 measurements randomly selected
from the population has a mean of 18.
Calculate the value of the test statistic Z.
By comparing Z with a critical value, test
H0 versus H1 at α = 0.05.
Calculate the p-value for testing H0 versus
H1.
Use the p-value to test H0 versus...

It is desired to test the null hypothesis µ = 40 against the
alternative hypothesis µ < 40 on the basis of a random sample
from a population with standard deviation 4. If the probability of
a Type I error is to be 0.04 and the probability of Type II error
is to be 0.09 for µ = 38, find the required size of the
sample.

The alternative hypothesis is H1: p < 0.15, and the test
statistic is z= -1.37 . Find p-value of the large sample one
proportion z-test.
Find critical value t a/2 for a one sample
t test to test H1: μ ≠ 5 at a significance level a=0.05
and degrees freedom = 15.
A company wants to determine if the average shearing strength
of all rivets manufactured is more than 1000 lbs. A sample of 25
rivets is selected and tested...

H0: µ ≥ 205 versus
H1:µ < 205, x= 198,
σ= 15, n= 20, α= 0.05
test
statistic___________ p-value___________ Decision
(circle one) Reject
the
H0 Fail
to reject the H0
H0: µ = 26 versus
H1: µ<> 26,x= 22,
s= 10, n= 30, α= 0.01
test
statistic___________ p-value___________ Decision
(circle one) Reject
the
H0 Fail
to reject the H0
H0: µ ≥ 155 versus
H1:µ < 155, x= 145,
σ= 19, n= 25, α= 0.01
test
statistic___________ p-value___________ Decision
(circle one) Reject
the
H0 Fail
to reject the H0

A hypothesis test is to be performed with a Null hypothesis
Ho: µ ≥ 15 and an alternative
hypothesis H1: µ <
15, the population standard deviation
is σ=2.0, the sample size is;
n=50, and the significance level is
α=0.025.
1- What is type l error?
2- What is the chance of making a type I error in the above
test?
3- What is a Type II error?
4- What value would the sample mean have to be less than to...

Compute the one sample Z-test for the following problems.
A test is conducted for H0: μ = 40, with σ = 5. A
sample size of 100 is selected X= 42.2
What is the null and alternative hypothesis for a 2-tailed test
of significance?
Compute the SEM for this problem.
Compute the one Sample Z-test for this problem.

A test of H0: µ = 7 versus H1: µ ≠ 7 does
not reject the null hypothesis at the 5% level. If calculated using
the same sample data, which of the following is a possible 95%
confidence interval for the population mean?
a.
9.2 ± 3.4
b.
8.4 ± 1.1
c.
There is not enough information to determine anything about a
95% confidence interval.
d.
6.2 ± 0.5

You want to test H0: µ ≤ 10.00 against H1: π > 10.00 using α
= 0.01, given that a sample of size = 25 found ?̅= 12.9 and s =
6.77.
a. What is the estimated standard error of ?̅, assuming that the
null hypothesis is correct?
b. Should your test statistic be a Z or a T (which, ZSTAT or
TSTAT)?
c. What is the attained value of the test statistic?
d. What is/are the critical values of...

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