Question

The female labor force participation rates (FLFPR) of women in randomly selected countries in 1990 and latest years of the 1990s are in the table below (Lim, 2002).  

Find differences in the direction of FLFPR 25-54 1990 minus FLFPR 25-54 Latest year of 1990s to complete your work and answer the given questions.

Region and country	FLFPR 25-54 1990	FLFPR 25-54 Latest year of 1990s
Iran	22.6	12.5
Morocco	41.4	34.5
Qatar	42.3	46.5
Syrian Arab Republic	25.6	19.5
United Arab Emirates	36.4	39.7
Cape Verde	46.7	50.9
Ghana	89.8	90.0
Kenya	82.1	82.6
Lesotho	51.9	68.0
South Africa	54.7	61.7
Bangladesh	73.5	60.6
Malaysia	49.0	50.2
Mongolia	84.7	71.3
Myanmar	72.1	72.3
Argentina	36.8	54
Belize	28.8	42.5
Bolivia	27.3	69.8
Brazil	51.1	63.2
Colombia	57.4	72.7
Ecuador	33.5	64
Nicaragua	50.1	42.5
Uruguay	59.5	71.5
Albania	77.4	78.8
Uzbekistan	79.6	82.8

#10. Estimate the mean difference in the female labor force participation rate in 1990 to latest years of the 1990s using a 95% confidence interval. Fill in blank 1 to report the bounds of the 95% CI. Enter your answers as lower bound,upper bound with no additional spaces and rounding bounds to two decimals.

Blank #1: 95% confident that the true mean difference in female labor force participation rates in 1990 to latest years of the 1990s is between _____________% and ___________________%.

#9. Do the data show that the mean female labor force participation rate in 1990 is different from that in the latest years of the 1990s using a 5% level of significance?

Use the framework below to guide your work.

Hypotheses: :     Ho: mu = 0; Ha: mu _____________0 (blank #2)

Blank #3: Test statistic = _________ (round to two decimal places)

Blank #4:  p-value = __________ (round to four decimal places)

Blank #5: Test decision: We decide to ___________ Ho (reject or do not reject)

Blank #6: Conclusion back into the words of problem: The evidence __________(favors or does not favor) that there is a difference in the female labor force participation rates in 1990 and the latest years of the 1990s.

Answer 1

Mean and variance are calculated by their usual formulas and hence I didn't show their calculations.

Please like. Thanks

Answer 2

DATA AND RANDOM VARIABLES-

Suppose, random variables X and Y denote female labor force participation rates in 1990 and latest year of 1990s respectively. Also, random variable D(=X-Y) denotes difference in female labor force participation rates.

Differences in the direction of female labor force participation rates in 1990 minus female labor force participation rates in latest year of 1990s are as follows.

HYPOTHESIS TEST-

Here, in two different instances (1990 and latest year of 1990s) female labor force participation rates were observed for same set of countries. So, we have to perform paired t-test.

We have to test for null hypothesis

against the alternative hypothesis

Our test statistic is given by

Here,

Number of pairs of observation

Mean difference is given by

Standard deviation of differences is given by

Degrees of freedom

[Using R-code 'pt(-1.97251,23)+1-pt(1.97251,23)']

Level of significance

We reject our null hypothesis if

Here, we observe that

So, we cannot reject our null hypothesis.

Hence, based on the given data we can conclude that there is no significant evidence that there is a difference in the female labor force participation rates between 1990 and the latest years of the 1990s.

CONFIDENCE INTERVAL-

Here, in two different instances (1990 and latest year of 1990s) female labor force participation rates were observed for same set of countries. So, we have to use test statistic corresponding to paired t-test.

Corresponding test statistic is given by

Here,

Number of pairs of observation

Mean difference is given by

Standard deviation of differences is given by

Degrees of freedom

We have,

[Using R-code 'qt(1-(1-0.95)/2,23)']

ANSWER-

10.

95% confident that the true mean difference in female labor force participation rates in 1990 to latest years of the 1990s is between -10.90956 % and 0.25956 %.

9.

Hypotheses are and

Test statistic = -1.97

p-value = 0.0607

Test decision: We decide to do not reject .

Conclusion back into the words of problem: The evidence does not favor that there is a difference in the female labor force participation rates in 1990 and the latest years of the 1990s.