Question

**Hypothesis Test for a Population Mean (σσ is
Unknown)**

You wish to test the following claim (HaHa) at a significance level
of α=0.10α=0.10.

Ho:μ=77.2Ho:μ=77.2

Ha:μ≠77.2Ha:μ≠77.2

You believe the population is normally distributed, but you do not
know the standard deviation. You obtain a sample of size n=83n=83
with mean M=78.9M=78.9 and a standard deviation of
SD=13.7SD=13.7.

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 p-value is...

less than (or equal to) αα

greater than αα

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 not equal to 77.2.

There is not sufficient evidence to warrant rejection of the claim that the population mean is not equal to 77.2.

The sample data support the claim that the population mean is not equal to 77.2.

There is not sufficient sample evidence to support the claim that the population mean is not equal to 77.2.

Answer #1

The statistical software output for this problem is:

**One sample T summary hypothesis test:**

μ : Mean of population

H_{0} : μ = 77.2

H_{A} : μ ≠ 77.2

**Hypothesis test results:**

Mean |
Sample Mean |
Std. Err. |
DF |
T-Stat |
P-value |
---|---|---|---|---|---|

μ | 78.9 | 1.5037704 | 82 | 1.1304918 | 0.2616 |

Hence,

Test statistic = 1.130

p-value = 0.2616

The p-value is greater than α

fail to reject the null

There is not sufficient sample evidence to support the claim that the population mean is not equal to 77.2.

You wish to test the following claim (HaHa) at a significance
level of α=0.10α=0.10.
Ho:μ=55.7Ho:μ=55.7
Ha:μ≠55.7Ha:μ≠55.7
You believe the population is normally distributed and you know the
standard deviation is σ=13.5σ=13.5. You obtain a sample mean of
¯x=60.9x¯=60.9 for a sample of size n=56n=56.
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 = Use Technology (Report answer accurate to 4
decimal places.)
The p-value...

You wish to test the following claim (HaHa) at a significance level
of α=0.10α=0.10.
Ho:μ=77.7Ho:μ=77.7
Ha:μ<77.7Ha:μ<77.7
You believe the population is normally distributed and you know the
standard deviation is σ=16.5σ=16.5. You obtain a sample mean of
M=74.8M=74.8 for a sample of size n=72n=72.
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 p-value...

You wish to test the following claim (Ha) at a significance
level of α=0.005.
Ho:μ=87.1
Ha:μ≠87.1
You believe the population is normally distributed, but you do not
know the standard deviation. You obtain a sample of size n=642 with
mean M=88.5 and a standard deviation of SD=13.1.
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...

You wish to test the following claim (HaHa) at a significance
level of α=0.05α=0.05.
Ho:μ=65.2Ho:μ=65.2
Ha:μ≠65.2Ha:μ≠65.2
You believe the population is normally distributed, but you do not
know the standard deviation. You obtain the following sample of
data:
data
14.6
36.1
13.5
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 p-value...

You wish to test the following claim (Ha) at a significance
level of α=0.02α=0.02.
Ho:μ=82.8
Ha:μ≠82.8
You believe the population is normally distributed and you know the
standard deviation is σ=12.7. You obtain a sample mean of M=76.1
for a sample of size n=21
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 p-value...

You wish to test the following claim (HaHa) at a significance
level of α=0.10α=0.10.
Ho:μ=80.9Ho:μ=80.9
Ha:μ<80.9Ha:μ<80.9
You believe the population is normally distributed, but you do not
know the standard deviation. You obtain a sample of size n=4n=4
with mean M=72.1M=72.1and a standard deviation of
SD=8.8SD=8.8.
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...

You wish to test the following claim (HaHa) at a significance
level of α=0.10α=0.10.
Ho:μ=61.2Ho:μ=61.2
Ha:μ>61.2Ha:μ>61.2
You believe the population is normally distributed, but you do not
know the standard deviation. You obtain a sample of size n=125n=125
with mean ¯x=66x¯=66 and a standard deviation of
s=14.1s=14.1.
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 4 decimal
places.)
The...

You wish to test the following claim (HaHa) at a significance
level of α=0.005α=0.005.
Ho:μ=54.3Ho:μ=54.3
Ha:μ>54.3Ha:μ>54.3
You believe the population is normally distributed. You obtain a
sample mean of 54.9 and a sample standard deviation of 8.2 for a
sample of size 72.
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 p-value is......

Hypothesis Test for the Difference in Population Means
(σσ Unknown)
You wish to test the following claim (HaHa) at a significance
level of α=0.005α=0.005.
Ho:μ1=μ2Ho:μ1=μ2
Ha:μ1>μ2Ha:μ1>μ2
You believe both populations are normally distributed, but you do
not know the standard deviations for either. Let's assume that the
variances of the two populations are not equal. You obtain the
following two samples of data.
Sample #1
60
62.8
60.2
48.5
61.8
52.7
65.1
66.3
71.4
72.2
63.8
59.5
70.5
58.3
79.6
57.4...

You wish to test the following claim (HaHa) at a significance
level of α=0.05α0.05.
Ho:μ=81.4Hoμ81.4
Ha:μ>81.4Haμ81.4
You believe the population is normally distributed, but you do not
know the standard deviation. You obtain a sample of size n=67n67
with mean M=87.9M87.9 and a standard deviation of
SD=20.4SD20.4.
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...

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