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
a)applying chi square goodness of fit test:
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 |
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.
Get Answers For Free
Most questions answered within 1 hours.