Question

suppose that we are testing H0:μ=μ0 versus H1:μμ0 with a sample size of n=10. calculate bounds on the P-value for the following observed values of the test statistic: a)t0 =2.48 b)t0=-3.95 c)t0=2.69 d)t0=1.88 e) t0=-1.25 Please show how the values were found

Engineering statistics 5th edition question 4-48

Answer #1

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):
(a) lower bound and (b) upper
bound upon t0 = -2.59,
(c) lower bound and (d) upper
bound upon t0 = -1.76,
(e) lower bound and (f) upper
bound upon t0...

Suppose that we are testing H0: μ =
μ0 versus H1: μ
< μ0. Calculate the P-value for the
following observed values of the test statistic:
(a)z0 = -2.31
(b)z0 = -1.76
(c)z0 = -2.50
(d)z0 = -1.48
(e)z0 = 0.63

Suppose we want to test H0: μ ≥ 30 versus H1: μ <30. Which of
the following possible sample results based on a sample size 36
provides the strongest evidence for rejecting H0 in favor of
H1?

To test H0: μ=100 versus H1: μ≠100, a simple random sample size
of n=24 is obtained from a population that is known to be normally
distributed.
A. If x=105.8 and s=9.3 compute the test statistic.
B. If the researcher decides to test this hypothesis at the
a=0.01 level of significance, determine the critical values.
C. Draw a t-distribution that depicts the critical regions.
D. Will the researcher reject the null hypothesis?
a. The researcher will reject the null hypothesis since...

Suppose we want to test H0 : μ ≥ 30 versus H1 : μ < 30. Which
of the following possible sample results based on a sample of size
36 gives the strongest evidence to reject H0 in favor of H1?
a) X¯=28,s=6
b) X¯=27,s=4
c) X¯=32,s=2
d) X¯=26,s=9

Suppose that you are testing the following hypotheses where the
variance is unknown: H0 : µ = 100 H0 : µ ≠ 100 The sample size is n
20. Find bounds on the P-value for the following values of the test
statistic. a. t0 = 2.75 b. t0 = 1.86 c. t0 = -2.05 d. t0 =
-1.86

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...

Suppose we have a random sample of size 50 from a N(μ,σ2) PDF.
We wish to test H0: μ=10 versus H1: μ=10. The sample moments are x
̄ = 13.4508 and s2 = 65.8016. (a) Find the critical region C and
test the null hypothesis at the 5% level. What is your decision?
(b) What is the p-value for your decision? (c) What is a 95%
confidence interval for μ?

The one-sample t statistic for testing H0: μ = 10 Ha: μ > 10
from a sample of n = 17 observations has the value t = 2.32.
(a) What are the degrees of freedom for this statistic?
(b) Give the two critical values t* from the t distribution
critical values table that bracket
? < t < ?
e) If you have software available, find the exact P-value.
(Round your answer to four decimal places.)

Suppose we have a random sample of size 50 from a N(μ,σ2) PDF.
We wish to test H0: μ=10 versus H1: μ=10. The sample moments are x
̄ = 13.4508 and s2 = 65.8016. (a) Test the null
hypothesis that σ2 = 64 versus a two-sided alternative. First, find
the critical region and then give your decision. (b) (5 points)
Find a 95% confidence interval for σ2? (c) (5 points) If you are
worried about performing 2 statistical tests on...

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