Solve the system of equations by substituion, -5x + y = 3 7.5x - 1.5y = 3
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Answer:
a) Point estimate p=0.43.
b) The 95% confidence interval for the population proportion of female workers in US is (0.388, 0.473).
c) This confidence interval tells us that, with 95% confidence, the true proportion of females in the U.S. labor force is within 0.388 and 0.473.
d) We can conclude that females do not make up a majority of the US labor force, because we can claim, with 95% confidence, that the true proportion of female workers is under 0.473, which is below 0.5 (or 50%).
Step-by-step explanation:
a) A point estimate can be calculated using the sample results and dividing the amount of female workers in the sample by the sample size:
b) We have to calculate a 95% confidence interval for the proportion.
The standard error of the proportion is:
The critical z-value for a 95% confidence interval is z=1.96.
The margin of error (MOE) can be calculated as:
Then, the lower and upper bounds of the confidence interval are:
The 95% confidence interval for the population proportion of female workers in US is (0.388, 0.473).
c) This confidence interval tells us that, with 95% confidence, the true proportion of females in the U.S. labor force is within 0.388 and 0.473.
d) We can conclude that females do not make up a majority of the US labor force, because we can claim, with 95% confidence, that the true proportion of female workers is under 0.473, which is below the 50%.
If the confidence interval have included the value 0.5, we could not be sure (with 95% confidence) that female workers do not represent de majority, as there would be possibility that the true proportion is 0.5.