Question

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 4 decimal places.)

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 greater than 80.2.
- There is not sufficient evidence to warrant rejection of the claim that the population mean is greater than 80.2.
- The sample data support the claim that the population mean is greater than 80.2.
- There is not sufficient sample evidence to support the claim that the population mean is greater than 80.2.

Answer #1

Solution:

1)

The test statistic t is

t = = [82.7 - 80.2]/[5.4 /55] = 3.433

**test statistic = 3.433**

2)

d.f. = n - 1 = 55 - 1 = 54

> sign in Ha indicates that the test is "One tailed right sided"

t = 3.433

So ,

**p value = 0.0006**

3)

The p-value is...

**less than (or equal to) αα**

4)

This test statistic leads to a decision to...

**reject the null**

5)

As such, the final conclusion is that...

**The sample data support the claim that the population
mean is greater than 80.2.**

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=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=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=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=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 =...

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=0.05α=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=0.005α=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 (Ha) at a significance
level of α=0.05
Ho:μ=84.2
Ha:μ<84.2
You believe the population is normally distributed, but you do not
know the standard deviation. You obtain a sample of size n=4 with
mean M=82.7 and a standard deviation of SD=6.1.
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=0.001α=0.001. For the context of this problem,
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the second data set represents a post-test.
Ho:μd=0Ho:μd=0
Ha:μd>0Ha:μd>0
You believe the population of difference scores is normally
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