Question

You wish to test the following claim (HaHa) at a significance
level of α=0.01α=0.01.

Ho:μ=72.8Ho:μ=72.8

Ha:μ>72.8Ha:μ>72.8

You believe the population is normally distributed and you know the
standard deviation is σ=5.8σ=5.8. You obtain a sample mean of
M=74.8M=74.8 for a sample of size n=46n=46.

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 greater than 72.8.
- There is not sufficient evidence to warrant rejection of the claim that the population mean is greater than 72.8.
- The sample data support the claim that the population mean is greater than 72.8.
- There is not sufficient sample evidence to support the claim that the population mean is greater than 72.8.

Answer #1

Given: n=46

M=74

At 1% level of significance we want to test the hypothesis that:

Z critical value at 1% level of significance for upper tail test is:

The test statistic is:

## Since population standard is known we used z test.

The test statistic is not in the critical region.

Since , we are unable to reject the null hypothesis.

Conclusion:

- There is not sufficient sample evidence to support the claim that the population mean is greater than 72.8.

You wish to test the following claim (HaHa) at a significance
level of α=0.01α=0.01.
Ho:μ=57.9Ho:μ=57.9
Ha:μ>57.9Ha:μ>57.9
You believe the population is normally distributed, but you do not
know the standard deviation. You obtain a sample of size n=52n=52
with a mean of M=60.1M=60.1 and a standard deviation of
SD=10.7SD=10.7.
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=0.01α=0.01.
Ho:μ=64.4Ho:μ=64.4
Ha:μ>64.4Ha:μ>64.4
You believe the population is normally distributed and you know the
standard deviation is σ=20.5σ=20.5. You obtain a sample mean of
M=70.7M=70.7 for a sample of size n=52n=52.
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=0.01α=0.01.
Ho:μ=68.7Ho:μ=68.7
Ha:μ<68.7Ha:μ<68.7
You believe the population is normally distributed and you know the
standard deviation is σ=5.5σ=5.5. You obtain a sample mean of
M=67.3M=67.3 for a sample of size n=18n=18.
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=0.01α=0.01.
Ho:μ=76.3Ho:μ=76.3
Ha:μ<76.3Ha:μ<76.3
You believe the population is normally distributed and you know the
standard deviation is σ=7.4σ=7.4. You obtain a sample mean of
M=73.6M=73.6 for a sample of size n=15n=15.
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=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=0.002α=0.002.
Ho:μ=72.9Ho:μ=72.9
Ha:μ>72.9Ha:μ>72.9
You believe the population is normally distributed, but you do not
know the standard deviation. You obtain a sample of size n=337n=337
with a mean of M=73.4M=73.4 and a standard deviation of
SD=19.3SD=19.3.
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=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=0.002α=0.002.
Ho:μ=54.2Ho:μ=54.2
Ha:μ>54.2Ha:μ>54.2
You believe the population is normally distributed, but you do not
know the standard deviation. You obtain a sample of size n=403n=403
with a mean of M=55.3M=55.3 and a standard deviation of
SD=7.4SD=7.4.
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=0.01α=0.01.
Ho:μ=69.7Ho:μ=69.7
Ha:μ<69.7Ha:μ<69.7
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=60.9M=60.9 and a standard deviation of
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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...

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