Question

You wish to test the following claim (Ha) at a significance
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
- 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 greater than 0.46.
- There is not sufficient evidence to warrant rejection of the claim that the population proportion is greater than 0.46.
- The sample data support the claim that the population proportion is greater than 0.46.
- There is not sufficient sample evidence to support the claim that the population proportion is greater than 0.46.

- There is sufficient evidence to warrant rejection of the claim that the population proportion is greater than 0.46.
- There is not sufficient evidence to warrant rejection of the claim that the population proportion is greater than 0.46.
- The sample data support the claim that the population proportion is greater than 0.46.
- There is not sufficient sample evidence to support the claim that the population proportion is greater than 0.46.

Answer #1

Solution:

Point estimate = sample proportion = = x / n = 0.497

This a right- tailed test.

Test statistics

z = ( - ) / *(1-) / n

= ( 0.497 - 0.46) / (0.46*0.54) / 648

= **1.885**

P-value = P(Z > z )

= 1 - P(Z < 1.885 )

= 1 - 0.9703

= **0.0297**

The p-value is p = 0.0297, and since **p = 0.0297 <
0.10,** it is concluded that the null hypothesis is
rejected.

**There is sufficient evidence to warrant rejection of the
claim that the population proportion is greater than
0.46.**

You wish to test the following claim a significance level of
α=0.10α=0.10.
Ho:p=0.46Ho:p=0.46
Ha:p<0.46Ha:p<0.46
You obtain a sample of size n=326n=326 in which there are 121
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
places.
The p-value is...
less than (or equal to) αα
greater than αα
This test statistic leads to a decision to...
reject the...

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=0.02α0.02.
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 =
What is the p-value for this sample? (Report...

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)...

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 a significance level of
α=0.001.
Ho:p=0.53
Ha:p>0.53
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?
P-value = Use Technology Round to 4 decimal
places.
The p-value is...
less than (or equal to) αα
greater than αα
This test statistic leads to a decision to...
reject the...

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?
P-value = Use Technology Round to 4 decimal
places.
The p-value is...
less than (or equal to) αα
greater than αα
This test statistic leads to a decision to...
reject the...

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
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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 (H1) at a significance
level of α=0.10.
Ho:p=0.33
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You obtain a sample of size n=357 in which there are 146 successful
observations.
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...

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α=0.01.
Ho:p=0.16
Ha:p<0.16
You obtain a sample of size n=649 in which there are 83
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What is the p-value for this sample?
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greater than αα
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