Question

You wish to test the following claim (HaHa) at a significance
level of α=0.05α=0.05.

Ho:μ=82.1Ho:μ=82.1

Ha:μ>82.1Ha:μ>82.1

You believe the population is normally distributed, but you do not
know the standard deviation. You obtain a sample of size n=16n=16
with mean M=90.8M=90.8 and a standard deviation of
SD=13.9SD=13.9.

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 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 greater than 82.1.
- There is not sufficient evidence to warrant rejection of the claim that the population mean is greater than 82.1.
- The sample data support the claim that the population mean is greater than 82.1.
- There is not sufficient sample evidence to support the claim that the population mean is greater than 82.1.

Answer #1

The null and alternatiev hypothesis is ,

(Claim)

Since , the population standard deviation is not known.

Therefore , use t-distribution.

Now df=degrees of freedom=n-1=16-1=15

The test statistic is ,

The p-value is ,

p-value= ; The Excel function is , =TDIST(2.5036,15,1)

The p-value is less than 0.05

This p-value leads to a decision to reject the null hypothesis.

Conclusion : There is not sufficient evidence to warrant rejection of the claim that the population mean is greater than 82.1.

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 (HaHa) at a significance
level of α=0.05α=0.05.
Ho:μ=63.1Ho:μ=63.1
Ha:μ>63.1Ha:μ>63.1
You believe the population is normally distributed, but you do not
know the standard deviation. You obtain a sample of size n=31n=31
with mean M=69.3M=69.3 and a standard deviation of
SD=10.4SD=10.4.
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...

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
Ha:μ>70.8Ha:μ>70.8
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
¯x=74.5x¯=74.5 for a sample of size n=31n=31.
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...

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...

You wish to test the following claim (HaHa) at a significance
level of α=0.005α=0.005.
Ho:μ=77.6Ho:μ=77.6
Ha:μ>77.6Ha:μ>77.6
You believe the population is normally distributed, but you do not
know the standard deviation. You obtain a sample of size n=11n=11
with mean M=89.6M=89.6 and a standard deviation of
SD=10.8SD=10.8.
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=0.10α=0.10.
Ho:μ=88.2Ho:μ=88.2
Ha:μ>88.2Ha:μ>88.2
You believe the population is normally distributed, but you do not
know the standard deviation. You obtain a sample of size n=27n=27
with mean M=92.6M=92.6 and a standard deviation of
SD=7.4SD=7.4.
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=0.005α=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......

You wish to test the following claim (HaHa) at a significance
level of α=0.10α=0.10.
Ho:μ=50.1Ho:μ=50.1
Ha:μ<50.1Ha:μ<50.1
You believe the population is normally distributed, but you do not
know the standard deviation. You obtain a sample of size n=20n=20
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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=0.01α=0.01.
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You believe the population is normally distributed, but you do not
know the standard deviation. You obtain a sample of size n=26n=26
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p-value =
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