Question

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 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 not equal to 89.3.
- There is not sufficient evidence to warrant rejection of the claim that the population mean is not equal to 89.3.
- The sample data support the claim that the population mean is not equal to 89.3.
- There is not sufficient sample evidence to support the claim that the population mean is not equal to 89.3.

Answer #1

Given that, sample size (n) = 75, sample mean = 94 and

population standard deviation = 13.2

The null and alternative hypotheses are,

H0 : μ = 89.3

H1 : μ ≠ 89.3 (claim)

This hypothesis test is a two-tailed test.

Test statistic is,

=> Test statistic = **3.084**

Using Excel we find, the p-value

Excel Command : = 2 * (1 - NORMSDIST(3.084)) = 0.0020

=> P-value = **0.0020**

The P-value is **less than (or equal to)** α

This test statistic leads to a decision 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 not equal to 89.3.**

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=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=51.3Ho:μ=51.3
H1:μ<51.3H1:μ<51.3
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
s=8.9s=8.9.
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=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...

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=0.01α=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=0.05α=0.05.
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
with mean M=64.7M=64.7 and a standard deviation of
SD=14.1SD=14.1.
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.
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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...

You wish to test the following claim (H1H1) at a significance
level of α=0.001α=0.001.
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test statistic =
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four decimal places.)
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