Question

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 =

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 70.8.

There is not sufficient evidence to warrant rejection of the claim that the population mean is greater than 70.8.

The sample data support the claim that the population mean is greater than 70.8.

There is not sufficient sample evidence to support the claim that the population mean is greater than 70.8.

Answer #1

Solution :

Given that ,

= 74.5

= 70.8

= 13.6

n = 31

= 0.05

Z_{}
= Z_{0.05} = 1.65

Critical value = 1.65

Test statistic = z = ( - ) / / n

= (74.5 - 70.8) / 13.6 / 31 = 1.515

Test statistic = 1.515

Test statistic < critical value

The test statistic is not in the critical region .

Fail to reject the null hypothesis .

There is not sufficient evidence to warrant rejection of the claim that the population mean is greater than 70.8.

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=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=88.5Ho:μ=88.5
Ha:μ≠88.5Ha:μ≠88.5
You believe the population is normally distributed and you know the
standard deviation is σ=12.6σ=12.6. You obtain a sample mean of
M=83M=83 for a sample of size n=53n=53.
What is the critical value for this test? (Report answer accurate
to three decimal places.)
critical value = ±±
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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=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=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
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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=0.10α=0.10.
Ho:μ=71.9Ho:μ=71.9
Ha:μ≠71.9Ha:μ≠71.9
You believe the population is normally distributed and you know the
standard deviation is σ=9.3σ=9.3. You obtain a sample mean of
M=74.5M=74.5 for a sample of size n=33n=33.
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=0.01α=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 =...

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
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know the standard deviation. You obtain a sample of size n=337n=337
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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
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know the standard deviation. You obtain a sample of size n=751n=751
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What is the critical value for this test? (Report answer accurate
to three decimal places.)
critical value =
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