Question

You wish to test the following claim (HaHa) at a significance
level of α=0.002α=0.002.

Ho:μ=86.2Ho:μ=86.2

Ha:μ>86.2Ha:μ>86.2

You believe the population is normally distributed, but you do not
know the standard deviation. You obtain a sample of size
n=14n=14with mean M=103.2M=103.2 and a standard deviation of
SD=16.7SD=16.7.

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 = _______

The p-value is...

A) less than (or equal to) α

or

B) greater than α

This test statistic leads to a decision to...

A) reject the null

B) accept the null

C) fail to reject the null

As such, the final conclusion is that...

A) There is sufficient evidence to warrant rejection of the claim that the population mean is greater than 86.2.

B) There is not sufficient evidence to warrant rejection of the claim that the population mean is greater than 86.2.

C) The sample data support the claim that the population mean is greater than 86.2.

D) There is not sufficient sample evidence to support the claim that the population mean is greater than 86.2.

Answer #1

**Solution:**

Test Hypothesis :

Ho : μ = 86.2

Ha : μ > 86.2

α = 0.02

Standard deviation SD = 13.3

Sample mean M = 103.2

Sample size n = 14

Test Statistic : Z = (M - μ)/(SD/√n)

= (103.2-86.2)/(13.3/√14)

= 17/3.55

= 4.7887

---------------------------------------------------------------------------

being a right tailed test, p-value = P(Z > 4.7887) = 0

α = 0.02

As p-value : 0 < α : 0.02 Reject null hypothesis.

The p-value is

B) greater than α

---------------------------------------------------------

This test statistic leads to a decision to...

A) reject the null

---------------------------------------------------------

As such, the final conclusion is that...

A) There is sufficient evidence to warrant rejection of the claim
that the population mean is greater than 86.2.

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=0.002α=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=0.002α=0.002.
Ho:μ=55.2Ho:μ=55.2
Ha:μ<55.2Ha:μ<55.2
You believe the population is normally distributed and you know the
standard deviation is σ=14.9σ=14.9. You obtain a sample mean of
¯x=47.2x¯=47.2 for a sample of size n=33n=33.
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 = Use Technology (Report answer accurate to 4...

ou wish to test the following claim (HaHa) at a significance
level of α=0.002α=0.002.
Ho:μ=57.2Ho:μ=57.2
Ha:μ<57.2Ha:μ<57.2
You believe the population is normally distributed and you know the
standard deviation is σ=6.2σ=6.2. You obtain a sample mean of
M=56.2M=56.2 for a sample of size n=15n=15.
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 (Ha) at a significance
level of α=0.002α=0.002.
Ho:μ=57.9
Ha:μ<57.9
You believe the population is normally distributed and you know the
standard deviation is σ=12.7σ=12.7. You obtain a sample mean of
M=54.2M=54.2 for a sample of size n=69n=69.
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=90.3Ho:μ=90.3
Ha:μ≠90.3Ha:μ≠90.3
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=102.6M=102.6 and a standard deviation of
SD=17.7SD=17.7.
1. What is the p-value for this sample? (Report answer accurate to
four decimal places.)
p-value = ___
2. The p-value is...
less than (or equal to) αα
greater than αα
3. This...

You wish to test the following claim (HaHa) at a significance
level of α=0.002α=0.002.
Ho:μ=68.3Ho:μ=68.3
Ha:μ≠68.3Ha:μ≠68.3
You believe the population is normally distributed, but you do not
know the standard deviation. You obtain a sample of size n=13n=13
with mean M=73.5M=73.5 and a standard deviation of
SD=13.4SD=13.4.
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=0.05α0.05.
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 (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 (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......

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