In 2014, the General Social Survey asked a respondents if they felt that science makes our lives healthier, easier and more comfortable. For men, 81.9% agreed and for women, 81.4% agreed. What is the point estimate of the difference in the population proportion of men and women who agreed?

The point estimate of the difference in proportion is the best guess value

of the difference between the two population proportions.

The given parameter are;

The survey question: If respondents felt that science makes our lives healthier.

The percentage (proportion) of men that agreed = 81.9%

The percentage (proportion) of women that agreed = 81.4%

Required:

The point estimate of the difference in the population proportion.

Solution:

The sample statistic of the difference in proportion is given by the difference in the proportion in the two population; p₂ - p₁ (a single value)

Therefore, the point estimate of the difference in the population proportion  of men and women is 81.9% - 81.4% = 0.5%.

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The point estimate of the difference in the population proportion of men and women who agreed is 0.005.

Explanation:

In statistic, point estimation comprises of the use of sample data to estimate a distinct data value (known as a point estimate) which is to function as a "best guess" or "best estimate" of an unidentified population parameter.  

The point estimate of the population mean (µ) is the sample mean ().

Similarly the point estimate of population proportion (p) is the sample proportion ().

In this case we need to estimate the point estimate of the difference in the population proportion of men and women who agreed.

The point estimate of the difference in the population proportion of men and women who agreed will be the difference between the sample proportions.

The sample proportion of men who agreed that they felt science makes our lives healthier, easier and more comfortable is,

The sample proportion of women who agreed that they felt science makes our lives healthier, easier and more comfortable is,

Compute the difference between the two sample proportions as follows:

Thus, the point estimate of the difference in the population proportion of men and women who agreed is 0.005.

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