91影视

In a sample of 1121 women, 23% said that they were aware of the fact that the Earth has lost half of its wildlife population during the past 50 years. In another sample of 1084 men, 26% said that they were aware that the Earth had lost half of its wildlife population during the past 50 years.

The 95% confidence interval for the difference between the two population proportions is (-0.0659, 0.00591).

a.

In general, the confidence interval for the difference between the two population proportions can be expressed as follows:

\(\left( {{{\hat p}_1} - {{\hat p}_2}} \right) - E < \left( {{p_1} - {p_2}} \right) < \left( {{{\hat p}_1} - {{\hat p}_2}} \right) + E\)

The confidence interval is equal to (-0.0659,0.00591).

Here, the value of -0.0659 (lower limit) is comparable to the expression\(\left( {{{\hat p}_1} - {{\hat p}_2}} \right) - E\).

Similarly, the value of 0.00591 (upper limit) is comparable to the expression \(\left( {{{\hat p}_1} - {{\hat p}_2}} \right) + E\).

Therefore, the expression of the confidence interval in terms of the symbol 鈥�<鈥� is given below:

\( - 0.0659 < \left( {{p_1} - {p_2}} \right) < 0.00591\)

b.

The confidence interval equal to (-0.0659, 0.00591) contains the value 0.

This suggests that the difference between the two population proportions can be equal to 0.

In simple words, the value of the population proportion of women who were aware of the statement can be equal to the population proportion of men who were aware of the statement.

Thus, there is not sufficient evidence to conclude that there is a significant difference in the proportion of women who were aware of the statement and the proportion of men who were aware of the statement.