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?
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.
To find the confidence interval for each sample, we will use the formula for a confidence interval:
Confidence Interval = Sample Statistic ± (Margin of Error)
For men:
Sample Statistic: 4.7%
Margin of Error: 0.8 percentage points
Confidence Interval for men = 4.7% ± 0.8
= (3.9%, 5.5%)
For women:
Sample Statistic: 5.9%
Margin of Error: 0.8 percentage points
Confidence Interval for women = 5.9% ± 0.8
= (5.1%, 6.7%)
To determine if the unemployment rate is higher amongst women than amongst men, we need to see if the confidence intervals for the two groups overlap or not.
Since the confidence interval for women's unemployment rate (5.1% to 6.7%) does not overlap with the confidence interval for men's unemployment rate (3.9% to 5.5%), we can conclude that the unemployment rate is statistically higher amongst women than amongst men.
To find the confidence interval for each sample statistic, we need to use the margin of error. The margin of error is the maximum likely difference between the sample statistic and the population parameter.
For the unemployment rate among men:
- Sample statistic: 4.7%
- Margin of error: 0.8 percentage points
To find the confidence interval, we need to subtract and add the margin of error to the sample statistic:
Lower Bound = Sample Statistic - Margin of Error
= 4.7% - 0.8% = 3.9%
Upper Bound = Sample Statistic + Margin of Error
= 4.7% + 0.8% = 5.5%
So, the confidence interval for the unemployment rate among men is 3.9% to 5.5%.
For the unemployment rate among women:
- Sample statistic: 5.9%
- Margin of error: 0.8 percentage points
Following the same process as above:
Lower Bound = Sample Statistic - Margin of Error
= 5.9% - 0.8% = 5.1%
Upper Bound = Sample Statistic + Margin of Error
= 5.9% + 0.8% = 6.7%
So, the confidence interval for the unemployment rate among women is 5.1% to 6.7%.
To answer whether the unemployment rate is higher among women than among men, we need to check if the confidence intervals overlap or not. If there is no overlap, it suggests a statistically significant difference between the two groups.
In this case, the confidence interval for the unemployment rate among women (5.1% to 6.7%) does not overlap with the confidence interval for men (3.9% to 5.5%). Therefore, based on this information, we can conclude that the unemployment rate is higher amongst women than amongst men.