In this scenario, 50% of the women aged 16 years and older in Country U were employed in the year 1985 and 59% of the women 16 and older in the year 2005.

Based on the given information, the following values are known:

Percentage A=50%Percentage B=59%Sample size A=50,000Sample size B=50,000

The question of statistically significant difference in percentages only makes sense when the sample is a probability sample.

On observing the given information, the sample is not known to be a probability sample, as the sample could contain all individuals in the population, and thus, the individuals were not selected from the population by chance. Therefore, this implies that the question does not make sense.

It is known from the results in Part (b) that the question does not make sense. In this context, it is known whether the samples are simple random samples.

This is not appropriate to answer the question as long as whether or not the samples are simple random samples.

The box corresponding to 1985 data contains a ticket per woman, where the value on the ticket is a 1, when she is employed. Otherwise, the value on the ticket is 0.

The box corresponding to 2005 data contains a ticket per woman, where the value on the ticket is a 1, when she is employed. Otherwise, the value on the ticket is 0.

The test hypotheses are given below:

Let μ be the population mean.

Null hypothesis: H0:μ=0

That is, the percentages of the two boxes are the same.

Alternative hypothesis: H1:μ≠0

That is, the percentages of the two boxes are different.

The standard deviation A is given below:

SE A=(Big number−Small number){Fraction with big number×Fraction with small number}=(1−0)0.5×(1−0.5)=(1−0)0.5×0.5=0.5

The standard error of Box A is given below:

SE Sum A=Sample size ×SD A=50,000×0.5=111.8034

The standard error A of the average is the standard error of the sum divided by the number of draws as given below:

SE avearge A=SE sum ANumber of draws×100%=111.803450,000×100%=0.22%

The standard deviation B is given below:

SE B=(Big number−Small number){Fraction with big number×Fraction with small number}=(1−0)0.59×(1−0.41)=(1−0)0.59×0.41=0.4918

The standard error of Box B is given below:

SE Sum B=Sample size ×SD B=50,000×0.4918=109.9698

The standard error B of the average is the standard error of the sum divided by the number of draws as given below:

SE avearge B=SE sum BNumber of draws×100%=109.969850,000×100%=0.22%

The standard error for the difference is shown below:

SE difference=(SE first quantity)2+((SE second quantity)2)=0.222+0.222=0.31%

The formula for test statistic is as follows:

z=Observed−ExpectedSE

Known values:

μ=0σ=0.31

The observed value, x is given below:

x=Percentage A−Percentage B=50%−59%=−9%

The z-score is obtained as given below:

z=−9−00.31=−29.05

The P-value is given below:

P=P(Z<−29.05 or Z>29.05)=1−[P(Z<29.05)−P(Z<−29.05)]

Using the Standard normal table, the value corresponding to P(Z<−29.05) is 0 and P(Z<29.05) is 1.

Remaining calculation:

P=1−[P(Z<29.05)−P(Z<−29.05)]=1−[1−0]=1−1=0

Since the P-value is less than any of level of significance, it is unusual to obtain a difference in sample percentages of 9% when there is no difference in the population percentages, and thus, the difference does not appear to be due to chance variation.

Therefore, this implies that the difference in percentages is statistically significant.