In: Math
The Australian Banking Association conducts a survey every five years into the status of women in the banking industry, including aspects relating to working hours. In the 1997 survey, which incorporated 705 respondents, 211 reported working more than 50 hours per week. Of the 620 respondents to the 2002 survey, 224 reported to be working in excess of 50 hours per week. The Australian Bankers Association is interested if there has been any change in work patterns and wished to test this proposition at the 10% level of significance.
1. If the hypotheses
are written in the form of the proportion in 1997 minus the
proportion in 2002, state the direction of the alternative
hypothesis used to test whether there has been a change in
attitudes. Type gt (greater than), ge (greater than or equal to),
lt (less than), le (less than or equal to) or ne (not equal to) as
appropriate in the box
2. Calculate the test statistic for the Z test correct to two
decimal places.
3. Use the tables in the text to determine the critical value used
to conduct the test. If there are two critical values, state only
the upper value.
4. Is the null hypothesis rejected for this test? Type yes or
no.
5. Hence, on the basis of this test, does there appear to have been
a change in the working patterns of women in the banking industry?
Type yes or no.
(1)
If the hypotheses are written in the form of the proportion in 1997 minus the proportion in 2002, the direction of the alternative hypothesis used to test whether there has been a change in attitudes is given by:
Explanation:
H0: Null Hypothesis: P1 = P2 (There has not been any change in work patterns)
HA: Alternative Hypothesis: P1 P2 (There has been any change in work patterns) (Claim)
(2)
n1 = 705
= 211/705 = 0.2993
n2 = 620
= 224/620 = 0.3613
Pooled Proportion is got as follows:
Test Statistic Z is got as follows:
So,
the test statistic for the Z test = - 2.40
(3)
= 0.10
Using the tables in the text to determine the critical value used to conduct the test = 1.645
Since there are two critical values, only the upper value is stated as follows:
1.645
(4)
Since calculated value of Z = - 2.40 is less than critical value of Z = - 1.645, the difference is significant. Reject null hypothesis.
So,
Correct option:
yes
(5)
Hence, on the basis of this test, there appears to have been a change in the working patterns of women in the banking industry.
So,
Correct option:
yes