Question

You wish to test the following claim (HaHa) at a significance
level of α=0.001α=0.001.

Ho:μ=67.9Ho:μ=67.9

Ha:μ<67.9Ha:μ<67.9

You believe the population is normally distributed and you know the
standard deviation is σ=10.2σ=10.2. You obtain a sample mean of
M=64.7M=64.7 for a sample of size n=36n=36.

What is the critical value for this test? (Report answer accurate
to three decimal places.)

critical value =

What is the test statistic for this sample? (Report answer accurate
to three decimal places.)

test statistic =

The test statistic is...

- in the critical region
- not in the critical region

This test statistic leads to a decision to...

- reject the null
- accept the null
- fail to reject the null

As such, the final conclusion is that...

- There is sufficient evidence to warrant rejection of the claim that the population mean is less than 67.9.
- There is not sufficient evidence to warrant rejection of the claim that the population mean is less than 67.9.
- The sample data support the claim that the population mean is less than 67.9.
- There is not sufficient sample evidence to support the claim that the population mean is less than 67.9.

Answer #1

The hypotheses are:

Ho:μ=67.9

Ha:μ<67.9

This is a one-sample z-test as the population standard deviation
is known.

σ=10.2

M = 64.7

At alpha = 0.001, the one-tailed z-critical value = -3.09

Test statistic = (M - 67.9)/(σ/√n)

= (64.7 - 67.9)/(10.2/6) = -1.882

The test statistic is not in the critical region as -1.882>-3.09

We fail to reject the null hypothesis.

The final conclusion is that:

There is not sufficient sample evidence to support the claim that
the population mean is less than 67.9

You wish to test the following claim (HaHa) at a significance
level of α=0.001α=0.001.
Ho:μ=81.1Ho:μ=81.1
Ha:μ>81.1Ha:μ>81.1
You believe the population is normally distributed, but you do not
know the standard deviation. You obtain a sample of size n=751n=751
with a mean of M=82M=82 and a standard deviation of
SD=11.9SD=11.9.
What is the critical value for this test? (Report answer accurate
to three decimal places.)
critical value =
What is the test statistic for this sample? (Report answer accurate
to three...

You wish to test the following claim (HaHa) at a significance
level of α=0.001α=0.001.
Ho:μ=82.7Ho:μ=82.7
Ha:μ≠82.7Ha:μ≠82.7
You believe the population is normally distributed, but you do not
know the standard deviation. You obtain the following sample of
data:
data
64.6
58.1
60.1
58.1
78.6
71.2
60.6
86.9
75.2
88.3
77.1
What is the critical value for this test? (Report answer accurate
to three decimal places.)
critical value = ±±
What is the test statistic for this sample? (Report answer accurate...

You wish to test the following claim (HaHa) at a significance
level of α=0.001α=0.001.
Ho:μ=61.4Ho:μ=61.4
Ha:μ<61.4Ha:μ<61.4
You believe the population is normally distributed, but you do not
know the standard deviation. You obtain the following sample of
data:
data
23.8
47.3
43
77.4
57.2
23.8
What is the test statistic for this sample? (Report answer accurate
to three decimal places.)
test statistic =
What is the p-value for this sample? (Report answer accurate to
four decimal places.)
p-value =
The...

You wish to test the following claim (HaHa) at a significance
level of α=0.001α=0.001.
Ho:μ=80.2Ho:μ=80.2
Ha:μ>80.2Ha:μ>80.2
You believe the population is normally distributed, but you do not
know the standard deviation. You obtain a sample of size n=55n=55
with mean ¯x=82.7x¯=82.7 and a standard deviation of
s=5.4s=5.4.
What is the test statistic for this sample?
test statistic = (Report answer accurate to 3 decimal
places.)
What is the p-value for this sample?
p-value = (Report answer accurate to...

You wish to test the following claim (HaHa) at a significance
level of α=0.001α=0.001.
Ho:μ=69.5Ho:μ=69.5
Ha:μ≠69.5Ha:μ≠69.5
You believe the population is normally distributed, but you do not
know the standard deviation. You obtain a sample of size n=26n=26
with mean M=67.8M=67.8 and a standard deviation of
SD=17.2SD=17.2.
What is the p-value for this sample? (Report answer accurate to
four decimal places.)
p-value =
The p-value is...
less than (or equal to) αα
greater than αα
This p-value leads to a...

You wish to test the following claim (HaHa) at a significance
level of α=0.001α=0.001.
Ho:μ=72.8Ho:μ=72.8
Ha:μ>72.8Ha:μ>72.8
You believe the population is normally distributed, but you do
not know the standard deviation.
data
123.7
125.2
127.8
What is the test statistic for this sample?
test statistic = Round to 3 decimal places
What is the p-value for this sample?
p-value = Round to 4 decimal places.
The p-value is...
less than (or equal to) αα
greater than αα
This test statistic leads...

ou wish to test the following claim (HaHa) at a significance
level of α=0.002α=0.002.
Ho:μ=57.2Ho:μ=57.2
Ha:μ<57.2Ha:μ<57.2
You believe the population is normally distributed and you know the
standard deviation is σ=6.2σ=6.2. You obtain a sample mean of
M=56.2M=56.2 for a sample of size n=15n=15.
What is the critical value for this test? (Report answer accurate
to three decimal places.)
critical value =
What is the test statistic for this sample? (Report answer accurate
to three decimal places.)
test statistic =...

You wish to test the following claim (Ha) at a significance
level of α=0.002α=0.002.
Ho:μ=57.9
Ha:μ<57.9
You believe the population is normally distributed and you know the
standard deviation is σ=12.7σ=12.7. You obtain a sample mean of
M=54.2M=54.2 for a sample of size n=69n=69.
What is the critical value for this test? (Report answer accurate
to three decimal places.)
critical value =
What is the test statistic for this sample? (Report answer accurate
to three decimal places.)
test statistic =...

You wish to test the following claim (HaHa) at a significance
level of α=0.05α=0.05.
Ho:μ=85.4Ho:μ=85.4
Ha:μ>85.4Ha:μ>85.4
You believe the population is normally distributed and you know the
standard deviation is σ=14.2σ=14.2. You obtain a sample mean of
M=88.2M=88.2 for a sample of size n=64n=64.
What is the critical value for this test? (Report answer accurate
to three decimal places.)
critical value =
What is the test statistic for this sample? (Report answer accurate
to three decimal places.)
test statistic =...

You wish to test the following claim (HaHa) at a significance
level of α=0.05α=0.05.
Ho:μ≤70.8Ho:μ≤70.8
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You believe the population is normally distributed and you know the
standard deviation is σ=13.6σ=13.6. You obtain a sample mean of
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What is the critical value for this test? (Report answer accurate
to two decimal places.)
critical value =
What is the standardized test statistic for this sample? (Report
answer accurate to three decimal places.)
test statistic...

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