Question

Assuming that, in testing H0:

μ

=20 vs. H1

μ

≠20, you decide on the critical region X bar ≤ 15 and

X bar ≥ 25. Assume X is normally distributed, σ

2

= 25, and the following four random values

are observed: 9, 20, 15, 11.

a) Would you accept or reject H

0

?

b) What level of

α

is assumed here?

c) What probability value would you report?

d) What would be the appropriate critical region for this problem if

α

=0.005? Would you reject

H

0

in this case?

Answer #1

You test the hypotheses H0: μ = 100 vs. H1: μ > 100,
and you reject H0 at α = .05. Is this enough information to know if
you will reject at α = .10? Explain.

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)?

3. Suppose you are testing H0 : = 10 vs H1 : 6= 10: The sample
is small (n = 5) and the data come from a normal population. The
variance, 2, is unknown. (a) Find the critical value(s)
corresponding to = 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)?

Suppose that we are to conduct the following hypothesis test:
H0: μ = 1080 , H1:μ >1080
Suppose that you also know that σ=240, n=100, x¯=1125.6, and
take α=0.005. Draw the sampling distribution, and use it to
determine each of the following:
A. The value of the standardized test statistic:
1.9 Note: For the next part, your answer should use interval
notation. An answer of the form (−∞,a) is expressed (-infty, a), an
answer of the form (b,∞) is expressed (b,...

Suppose that you are testing the hypotheses H0: μ=12 vs. HA:
μless than<12. A sample of size 25 results in a sample mean of
12.5 and a sample standard deviation of 1.9. a) What is the
standard error of the mean? b) What is the critical value of t*
for a 90% confidence interval? c) Construct a 90% confidence
interval for μ. d) Based on the confidence interval, at
alphaαequals=0.05 can you reject H0? Explain.

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

For each of the following testing scenarios, select your answer
regarding the decision.
(b) H0 : μ = 25 vs. H1 : μ 6= 25 at level a = 0:10.
i. Reject H0
ii. Do not reject H0
iii. Can’t tell
(c) H0 : μ = 25 vs. H1 : μ 6= 25 at level a = 0:05.
i. Do not reject H0
ii. Reject H0
iii. Can’t tell

Suppose that we are to conduct the following hypothesis
test:
H0: μ=990
H1:μ>990
Suppose that you also know that σ=220, n=100, x¯=1031.8, and
take α=0.01.
Draw the sampling distribution, and use it to determine each of
the following:
A. The value of the standardized test statistic:
Note: For the next part, your answer should use interval
notation.
An answer of the form (−∞,a) is expressed (-infty, a), an answer
of the form (b,∞) is expressed (b, infty), and an answer...

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

1.
a) For a test of
H0 : μ = μ0
vs.
H1 : μ ≠
μ0,
the value of the test statistic z obs is
-1.46. What is the p-value of the hypothesis test?
(Express your answer as a decimal rounded to three decimal
places.)
I got 0.101
b) Which of the following is a valid alternative hypothesis for
a one-sided hypothesis test about a population mean μ?
a
μ ≠ 5.4
b
μ = 3.8
c
μ <...

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