Question

Suppose that we wish to test H_{0}: µ = 20 versus
H_{1}: 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 H_{0}versus H_{1}at α = 0.05. - Calculate the
*p*-value for testing H_{0}versus H_{1}. - Use the
*p*-value to test*H*_{0}versus H_{1}at each of α =0.10, 0.05, 0.01, and 0.001. - How much evidence is there that H
_{0}: µ = 20 is false?

**Answers should be in word version**

Answer #1

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

H0: µ ≥ 20 versus H1: µ < 20, α = 0.05, sample mean = 19, σ =
5, n = 25

We wish to test H0: μ = 120 versus Ha:
μ ¹ 120, where ? is known to equal 14. The sample of n = 36
measurements randomly selected from the population has a mean of ?̅
= 15.
a. Calculate the value of the test
statistic z.
b. By comparing z with a critical
value, test H0 versus Ha at ? = .05.

. 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...

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...

7. Suppose you are testing H0 : µ = 10 vs H1 : µ 6= 10. The
sample is small (n = 5) and the data come from a normal population.
The variance, σ 2 , is unknown. (a) Find the critical value(s)
corresponding to α = 0.10. (b) You find that t = −1.78. Based on
your critical value, what decision do you make regarding the null
hypothesis (i.e. do you Reject H0 or Do Not Reject H0)?

We want to test H0 : µ ≤ 120 versus Ha : µ > 120 . We know
that n = 324, x = 121.100 and, σ = 9. We want to test H0 at the .05
level of significance. For this problem, round your answers to 3
digits after the decimal point.
1. What is the value of the test statistic?
2. What is the critical value for this test?
3. Using the critical value, do we reject or...

Suppose that we are testing H0: μ = μ0 versus H1: μ < μ0 with
sample size of n = 25. Calculate bounds on the P -value for the
following observed values of the test statistic (use however many
decimal places presented in the look-up table. Answers are
exact):
(h) upper bound upon t0 = -1.3.
THE ANSWER IS NOT 0.15 OR 0.05

To test H0: σ=70 versus H1: σ<70, a random sample of size n
equals 25 is obtained from a population that is known to be
normally distributed.
(a) If the sample standard deviation is determined to be s
equals = 46.5, compute the test statistic.
(b) If the researcher decides to test this hypothesis at α=0.05
level of significance, use technology to determine the
P-value.
(c) Will the researcher reject the null hypothesis?
What is the P-Value?

1. For testing H0 : µ = 0 vs. Ha : µ > 0, H0 is rejected if X
>¯ 1.645, given n = 36 and σ = 6. What is the value of α, i.e.,
maximum probability of Type I error?
A. 0.90 B. 0.10 C. 0.05 D. 0.01
2. For testing H0 : µ = 0 vs. Ha : µ > 0, H0 is rejected if X
>¯ 1.645, given n = 36 and σ = 6. What...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 11 minutes ago

asked 17 minutes ago

asked 23 minutes ago

asked 26 minutes ago

asked 26 minutes ago

asked 31 minutes ago

asked 49 minutes ago

asked 56 minutes ago

asked 59 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago