Suppose that a random sample of 100 men between the ages of 25 and 54 was select

Question

Suppose that a random sample of 100 men between the ages of 25 and 54 was selected and it was found that 84 were currently working. A similar sample of 100 women was selected and 70 were working. Complete parts a and b below.
a. Using alphaequals 0.10?, can it be concluded that the proportion of men in this age group who are working differs from the proportion of women who are? working?

What is the test? statistic?
chi squaredequals
nothing ?(Round to two decimal places as? needed.)

What is the critical? value?
chi Subscript alpha Superscript 2equals
nothing ?(Round to two decimal places as? needed.)
What is the correct? conclusion?
?
Reject
Do not reject
Upper H 0. There
?
is not
is
enough evidence to conclude that the proportion of men in this age group who are working differs from the proportion of women who are working.
b. Determine the? p-value for the? chi-square test statistic and interpret its meaning.
What is the? p-value?
?p-valueequals
nothing ?(Round to three decimal places as? needed.)
What does the? p-value mean? Select the correct choice and fill in the answer box to complete your choice.
?(Round to one decimal places as? needed.)
A.
Given a very large number of? samples, there is a
nothing?% chance of observing a sample with the given data.
B.
There is a
nothing?% chance of rejecting the null hypothesis when it should not be rejected.
C.
There is a
nothing?% chance of observing a test statistic value greater than the actual value of this test statistic if there is no difference in the working proportions.
D.
There is a
nothing?% margin of error for the accuracy of this data

Explanation / Answer

a)applying chi square goodness of fit test:

chi squared test statistic =5.53

critical value =2.71

correct  conclusion -- Reject Ho

There is enough evidence to conclude that the proportion of men in this age group who are working differs from the proportion of women who are working.

b)

p value =0.019

There is a 1.9 % chance of observing a test statistic value greater than the actual value of this test statistic if there is no difference in the working proportions.

Observed Oi working not working Total men 84 16 100 women 70 30 100 Total 154 46 200 Expected Ei=?row*?column/?total working not working Total men 77.000 23.000 100 women 77.000 23.000 100 Total 154 46 200 chi square =(Oi-Ei)2/Ei working not working Total men 0.636 2.130 2.767 women 0.636 2.130 2.767 Total 1.273 4.261 5.534

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