Question

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

Ho:p=0.58Ho:p=0.58

Ha:p≠0.58Ha:p≠0.58

You obtain a sample of size n=720n=720 in which there are 455
successful observations.

Determine the test statistic formula for this test.

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 proportion is not equal to 0.58.
- There is not sufficient evidence to warrant rejection of the claim that the population proportion is not equal to 0.58.
- The sample data support the claim that the population proportion is not equal to 0.58.
- There is not sufficient sample evidence to support the claim that the population proportion is not equal to 0.58.

Answer #1

P = X / n = 455/720 = 0.6319

Test Statistic :-

Z = ( P - P0 ) / ( √((P0 * q0)/n)

Z = ( 0.6319 - 0.58 ) / ( √(( 0.58 * 0.42) /720))

Z = 2.824

P value = 2 * P ( Z > 2.824 ) = 0.0047 ( From Z table )

Reject null hypothesis if P value < α = 0.001

Since P value = 0.0047 > 0.001, hence we fail to reject the null
hypothesis

**Conclusion :- We Fail to Reject H0**

greater than αα

fail to reject the null

There is sufficient evidence to warrant rejection of the claim that the population proportion is not equal to 0.58.

You wish to test the following claim (HaHa) at a significance
level of α=0.01
Ho:p=0.89
Ha:p<0.89
You obtain a sample of size n=526 in which there are 461 successful
observations.
Determine the test statistic formula for this test.
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)...

You wish to test the following claim (HaHa) at a significance
level of α=0.002α=0.002.
Ho:p=0.22Ho:p=0.22
Ha:p≠0.22Ha:p≠0.22
You obtain a sample of size n=536n=536 in which there are 146
successful observations.
Determine the test statistic formula for this test.
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)...

You wish to test the following claim (HaHa) at a significance
level of α=0.02α0.02.
Ho:p=0.22Hop0.22
Ha:p<0.22Hap0.22
You obtain a sample of size n=167n167 in which there are 22
successful observations. For this test, you should NOT use the
continuity correction, and you should use the normal distribution
as an approximation for the binomial distribution.
What is the test statistic for this sample? (Report answer accurate
to three decimal places.)
test statistic =
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you wish to test the following claim (HaHa) at a significance
level of α=0.01α=0.01.
Ho:p=0.14Ho:p=0.14
Ha:p<0.14Ha:p<0.14
You obtain a sample of size n=709n=709 in which there are 94
successful observations. For this test, you should NOT use the
continuity correction, and you should use the normal distribution
as an approximation for the binomial distribution.
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...

You wish to test the following claim (HaHa) at a significance
level of ?=0.002.
Ho:p=0.18
Ha:p?0.18
You obtain a sample of size n=435 in which there are 73 successful
observations. For this test, you should NOT use the continuity
correction, and you should use the normal distribution as an
approximation for the binomial distribution.
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...

You wish to test the following claim at a significance level of
α=0.001α=0.001.
Ho:p=0.24Ho:p=0.24
Ha:p<0.24Ha:p<0.24
You obtain a sample of size n=695n=695 in which there are 139
successful observations.
What is the test statistic for this sample?
test statistic = Round to 3 decimal places.
What is the p-value for this sample?
P-value = Use Technology Round to 4 decimal
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The p-value is...
less than (or equal to) α
greater than α
This test statistic leads to a decision to...
reject...

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level of α=0.10
Ho:p=0.46
Ha:p>0.46
You obtain a sample of size n=648in which there are 322 successful
observations.
Determine the test statistic formula for this test.
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...

You wish to test the following claim a significance level of
α=0.001.
Ho:p=0.53
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You obtain a sample of size n=165 in which there are 94
successful observations.
What is the test statistic for this sample?
test statistic = Round to 3 decimal places.
What is the p-value for this sample?
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The p-value is...
less than (or equal to) αα
greater than αα
This test statistic leads to a decision to...
reject the...

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level of ?=0.01.
Ho:p=0.3
Ha:p<0.3
You obtain a sample of size n=452 in which there are 128 successful
observations. For this test, you should NOT use the continuity
correction, and you should use the normal distribution as an
approximation for the binomial distribution.
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...

You wish to test the following claim a significance level of
α=0.005.
Ho:p=0.71
Ha:p≠0.71
You obtain a sample of size n=164 in which there are 111
successful observations.
What is the test statistic for this sample?
test statistic = Round to 3 decimal places.
What is the p-value for this sample?
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places.
The p-value is...
less than (or equal to) αα
greater than αα
This test statistic leads to a decision to...
reject the...

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