To find the confidence interval, we use the sample statistic and the margin of error.
For men: Sample statistic = 4.7%, Margin of error = 0.8 percentage points.
The lower bound of the confidence interval for men is 4.7% - 0.8% = 3.9%
The upper bound of the confidence interval for men is 4.7% + 0.8% = 5.5%
For women: Sample statistic = 5.9%, Margin of error = 0.8 percentage points.
The lower bound of the confidence interval for women is 5.9% - 0.8% = 5.1%
The upper bound of the confidence interval for women is 5.9% + 0.8% = 6.7%
To determine if we can conclude that the unemployment rate is higher among women than among men, we need to check if the confidence intervals of the two groups overlap or not.
The confidence interval for men is 3.9% to 5.5%.
The confidence interval for women is 5.1% to 6.7%.
Since the confidence intervals overlap, we cannot conclude definitively that the unemployment rate is higher amongst women than amongst men.
A sample statistic and margin of error are given. Find the confidence interval likely to contain the population parameter of interest and answer the question. In a survey conducted in a certain city it was found that 4.7% of men and 5.9% of women were unemployed. The margin of error for each reported was 0.8 percentage points. Use each sample static to find a confidence interval. Can we conclude that the unemployment rate is higher amongst women than amongst men?
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