Question

You wish to test the following claim (H1H1) at a significance
level of α=0.01α=0.01.

Ho:μ=71.3Ho:μ=71.3

H1:μ>71.3H1:μ>71.3

You believe the population is normally distributed, but you do not
know the standard deviation. You obtain a sample of size n=33n=33
with mean M=78.3M=78.3 and a standard deviation of
SD=18.3SD=18.3.

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 greater than 71.3.
- There is not sufficient evidence to warrant rejection of the claim that the population mean is greater than 71.3.
- The sample data support the claim that the population mean is greater than 71.3.
- There is not sufficient sample evidence to support the claim that the population mean is greater than 71.3.

Answer #1

Test Statistic :-

t = ( X̅ - µ ) / (S / √(n) )

t = ( 78.3 - 71.3 ) / ( 18.3 / √(33) )

t = 2.197

P - value = P ( t > 2.1974 ) = 0.0177

Reject null hypothesis if P value < α = 0.01 level of
significance

P - value = 0.0177 > 0.01 ,hence we fail to reject null
hypothesis

**Conclusion :- Fail to reject null
hypothesis**

P value **is greater than α**

This test statistic leads to a decision to...

- fail to reject the null

Conclusion :- There is sufficient evidence to warrant rejection of the claim that the population mean is greater than 71.3.

You wish to test the following claim (H1H1) at a significance
level of α=0.01α=0.01.
Ho:μ=65.1Ho:μ=65.1
H1:μ>65.1H1:μ>65.1
You believe the population is normally distributed, but you do not
know the standard deviation. You obtain a sample of size n=740n=740
with mean M=66.1M=66.1 and a standard deviation of
SD=17.1SD=17.1.
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 (H1H1) at a significance
level of α=0.01α=0.01.
Ho:μ=82.5Ho:μ=82.5
H1:μ≠82.5H1:μ≠82.5
You believe the population is normally distributed, but you do not
know the standard deviation. You obtain a sample of size n=449n=449
with mean M=81.7M=81.7 and a standard deviation of
SD=10.7SD=10.7.
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...

You wish to test the following claim (H1H1) at a significance
level of α=0.01α=0.01.
Ho:μ=79.5Ho:μ=79.5
H1:μ<79.5H1:μ<79.5
You believe the population is normally distributed, but you do not
know the standard deviation. You obtain a sample of size n=637n=637
with mean ¯x=79x¯=79and a standard deviation of s=10.3s=10.3.
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 (H1H1) at a significance
level of α=0.01α=0.01.
Ho:μ=69.9Ho:μ=69.9
H1:μ>69.9H1:μ>69.9
You believe the population is normally distributed, but you do not
know the standard deviation. You obtain the following sample of
data:
data
77.2
76.4
66.7
68.1
66
69.2
81.3
76.2
74.9
70.9
78.3
70.2
76.2
73.2
68.8
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?...

You wish to test the following claim (H1H1) at a significance
level of α=0.05α=0.05.
Ho:μ=89.5Ho:μ=89.5
H1:μ>89.5H1:μ>89.5
You believe the population is normally distributed, but you do not
know the standard deviation. You obtain a sample of size n=61n=61
with mean M=92.6M=92.6 and a standard deviation of
SD=12.3SD=12.3.
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 (H1H1) at a significance
level of α=0.002α=0.002.
Ho:μ=63.9Ho:μ=63.9
H1:μ<63.9H1:μ<63.9
You believe the population is normally distributed, but you do not
know the standard deviation. You obtain the following sample of
data:
data
82.5
57.8
79.7
47.4
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 =
The p-value is......

You wish to test the following claim (H1H1) at a significance
level of α=0.002α=0.002.
Ho:μ=89.3Ho:μ=89.3
H1:μ≠89.3H1:μ≠89.3
You believe the population is normally distributed and you know the
standard deviation is σ=13.2σ=13.2. You obtain a sample mean of
¯x=94x¯=94 for a sample of size n=75n=75.
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 (H1H1) at a significance
level of α=0.002α=0.002.
Ho:μ=89.3Ho:μ=89.3
H1:μ≠89.3H1:μ≠89.3
You believe the population is normally distributed and you know the
standard deviation is σ=13.2σ=13.2. You obtain a sample mean of
¯x=94x¯=94 for a sample of size n=75n=75.
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 (H1H1) at a significance
level of α=0.002α=0.002.
Ho:μ=51.3Ho:μ=51.3
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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=627n=627
with mean ¯x=49.8x¯=49.8 and a standard deviation of
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What is the test statistic for this sample? (Report answer accurate
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test statistic =
What is the p-value for this sample? (Report answer accurate to
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Ho:μ=67.1Ho:μ=67.1
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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=97n=97
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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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