Question

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

Ho:μ=82.3Ho:μ=82.3

H1:μ>82.3H1:μ>82.3

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 a mean of ¯x=90x¯=90 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 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 82.3.
- There is not sufficient evidence to warrant rejection of the claim that the population mean is greater than 82.3.
- The sample data support the claim that the population mean is greater than 82.3.
- There is not sufficient sample evidence to support the claim that the population mean is greater than 82.3.

Answer #1

Given that, sample size (n) = 26, sample mean = 90 and

sample standard deviation (s) = 11.9

The null and alternative hypotheses are,

H0 : μ = 82.3

H1 : μ > 82.3

This test is right-tailed test,

Degrees of freedom = 26 - 1 = 25

t-critical value at significance level of 0.001 is, t* = 3.450

=> Critical value = **3.450**

Test statistic is,

=> test statistic = **3.299**

Since, test statistic = 3.299 < 3.450,

The test statistic is **not in the critical
region.**

This test statistic leads to a decision to **fail to
reject the null.**

As such, the final conclusion is that, **There is not
sufficient sample evidence to support the claim that the population
mean is greater than 82.3.**

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 (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 (H1) at a significance
level of α=0.01.
Ho:μ=82.6
H1:μ>82.6
You believe the population is normally distributed, but you do not
know the standard deviation. You obtain the following sample of
data:
data
84.2
79.3
95
87.8
81.6
86.2
82.9
112.6
102.1
85
96.7
67.3
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...

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=0.001α=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...

You wish to test the following claim (H1H1) at a significance
level of α=0.10α=0.10.
Ho:μ=79.9Ho:μ=79.9
H1:μ≠79.9H1:μ≠79.9
You believe the population is normally distributed, but you do not
know the standard deviation. You obtain a sample of size n=331n=331
with a mean of M=80.6M=80.6 and a standard deviation of
SD=8.2SD=8.2.
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...

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 (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=65.1Ho:μ=65.1
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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=740n=740
with mean M=66.1M=66.1 and a standard deviation of
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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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