Question

A researcher investigated determinants that account for individuals' making a transition from having a home (domiciled) but using meal programs to becoming homeless. The following table contains the data obtained in the study.

Homeless Men | Domiciled Men | |
---|---|---|

Sample size | 117 | 267 |

Number currently working | 33 | 96 |

Is there sufficient evidence to indicate that the proportion of those currently working is larger for domiciled men than for homeless men? (Use

*α* = 0.01.

Use

*p*_{1}

for the population proportion of homeless men who are currently working and

*p*_{2}

for the population proportion of domiciled men who are currently working.)

State the null and alternative hypotheses.

*H*_{0}: *p*_{1} ≠
*p*_{2}

*H*_{a}: *p*_{1} =
*p*_{2}

*H*_{0}: *p*_{1} >
*p*_{2}

*H*_{a}: *p*_{1} =
*p*_{2}

*H*_{0}: *p*_{1} =
*p*_{2}

*H*_{a}: *p*_{1} ≠
*p*_{2}

*H*_{0}: *p*_{1} =
*p*_{2}

*H*_{a}: *p*_{1} >
*p*_{2}

*H*_{0}: *p*_{1} =
*p*_{2}

*H*_{a}: *p*_{1} <
*p*_{2}

State the rejection region. (Assume the test statistic will be calculated using homeless men − domiciled men. Round your answers to two decimal places. If the test is one-tailed, enter NONE for the unused region.)

*z* > ___

*z* < ___

Calculate the appropriate test statistic. (Calculate the test statistic using homeless men − domiciled men. Round your answer to two decimal places.)

* z* =

What is the conclusion of your test?

Fail to reject *H*_{0}. There is not
sufficient evidence to indicate that the proportion of those
currently working is larger for domiciled men than for homeless
men.

Reject *H*_{0}. There is not sufficient
evidence to indicate that the proportion of those currently working
is larger for domiciled men than for homeless
men.

Fail to reject *H*_{0}. There is
sufficient evidence to indicate that the proportion of those
currently working is larger for domiciled men than for homeless
men.

Reject *H*_{0}. There is sufficient
evidence to indicate that the proportion of those currently working
is larger for domiciled men than for homeless men.

Answer #1

H0: p1 = p2

Ha: p1 < p2

This is left tailed test, for α = 0.01

Critical value of z is -2.33.

Hence reject H0 if z < -2.33

z > NONE

p1cap = X1/N1 = 33/117 = 0.2821

p1cap = X2/N2 = 96/267 = 0.3596

pcap = (X1 + X2)/(N1 + N2) = (33+96)/(117+267) = 0.3359

Test statistic

z = (p1cap - p2cap)/sqrt(pcap * (1-pcap) * (1/N1 + 1/N2))

z = (0.2821-0.3596)/sqrt(0.3359*(1-0.3359)*(1/117 + 1/267))

z = -1.48

Fail to reject H0. There is not sufficient evidence to indicate
that the proportion of those currently working is larger for
domiciled men than for homeless men.

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