Question

You wish to test the following claim (HaHa) at a significance
level of α=0.01α=0.01.

Ho:p1=p2Ho:p1=p2

Ha:p1<p2Ha:p1<p2

You obtain a sample from the first population with 294 successes
and 167 failures. You obtain a sample from the second population
with 402 successes and 200 failures. 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 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 first population proportion is less than the second population proportion.
- There is not sufficient evidence to warrant rejection of the claim that the first population proportion is less than the second population proportion.
- The sample data support the claim that the first population proportion is less than the second population proportion.
- There is not sufficient sample evidence to support the claim that the first population proportion is less than the second population proportion.

Answer #1

Pop 1 | Pop 2 | |

x= | 294 | 402 |

n = | 461 | 602 |

p̂=x/n= | 0.6377 | 0.6678 |

estimated prop. diff
=p̂_{1}-p̂_{2} = |
-0.0300 | |

pooled prop p̂
=(x_{1}+x_{2})/(n_{1}+n_{2})= |
0.6548 | |

std error Se=√(p̂1*(1-p̂1)*(1/n1+1/n2) = | 0.0294 | |

test stat z=(p̂1-p̂2)/Se = |
-1.021 |

P value = |
0.1537 |
(from excel:1*normsdist(-1.02) |

the p value is less than α

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

There is not sufficient sample evidence to support the claim that
the first population proportion is less than the second population
proportion.

You wish to test the following claim (HaHa) at a significance
level of α=0.01α=0.01.
Ho:p1=p2Ho:p1=p2
Ha:p1≠p2Ha:p1≠p2
You obtain 26.5% successes in a sample of size n1=686n1=686 from
the first population. You obtain 34.9% successes in a sample of
size n2=476n2=476 from the second population. 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...

You wish to test the following claim (HaHa) at a significance
level of α=0.01α=0.01.
Ho:p1=p2Ho:p1=p2
Ha:p1≠p2Ha:p1≠p2
You obtain 26.5% successes in a sample of size n1=686n1=686 from
the first population. You obtain 34.9% successes in a sample of
size n2=476n2=476 from the second population. 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...

You wish to test the following claim (HaHa) at a significance
level of α=0.02α=0.02.
Ho:p1=p2Ho:p1=p2
Ha:p1≠p2Ha:p1≠p2
You obtain 75.1% successes in a sample of size n1=618 from the
first population. You obtain 71.1% successes in a sample of size
n2=629 from the second population. 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...

You wish to test the following claim (HaHa) at a significance
level of α=0.005α=0.005.
Ho:p1=p2Ho:p1=p2
Ha:p1<p2Ha:p1<p2
You obtain 14.9% successes in a sample of size n1=456n1=456 from
the first population. You obtain 17.5% successes in a sample of
size n2=480n2=480 from the second population. 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...

You wish to test the following claim (HaHa) at a significance
level of α=0.005α=0.005.
Ho:p1=p2Ho:p1=p2
Ha:p1>p2Ha:p1>p2
You obtain 69.3% successes in a sample of size n1=722n1=722 from
the first population. You obtain 56.6% successes in a sample of
size n2=221n2=221 from the second population. 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...

You wish to test the following claim (HaHa) at a significance
level of α=0.001α=0.001.
Ho:p1=p2Ho:p1=p2
Ha:p1≠p2Ha:p1≠p2
You obtain 254 successes in a sample of size n1=387n1=387 from the
first population. You obtain 167 successes in a sample of size
n2=236n2=236 from the second population. 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...

You wish to test the following claim (Ha) at a significance
level of α=0.05.
Ho:p1=p2
Ha:p1<p2
You obtain a sample from the first population with 61 successes and
612 failures. You obtain a sample from the second population with
78 successes and 575 failures. 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...

You wish to test the following claim (HaHa) at a significance
level of α=0.10.
Ho:p1=p2
Ha:p1>p2
You obtain 84 successes in a sample of size n1=556 from the first
population. You obtain 73 successes in a sample of size n2=725 from
the second population. 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...

You wish to test the following claim (HaHa) at a significance
level of α=0.10α=0.10.
Ho:p1=p2
Ha:p1≠p2
You obtain 42.7% successes in a sample of size n1=321n1=321 from
the first population. You obtain 37.7% successes in a sample of
size n2=281n2=281 from the second population. 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...

You wish to test the following claim (HaHa) at a significance
level of α=0.01α=0.01.
Ho:p1=p2Ho:p1=p2
Ha:p1>p2Ha:p1>p2
You obtain 71 successes in a sample of size n1=715n1=715 from the
first population. You obtain 34 successes in a sample of size
n2=679n2=679 from the second population. 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...

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