A random sample of 50 house holds in community A has a mean house hold income of mean = $44600 with a standard devation =2200 A random sample of 50 house holds in community B has a mean of $43800 with astandar devation of $2800. Estimate the difference in the average house hold income in the two communities using a 95 percent cofidence interval.
To estimate the difference in the average household income between the two communities using a 95% confidence interval, you can follow these steps:
Step 1: Calculate the standard error of the difference between the means.
The standard error of the difference between two sample means can be calculated using the following formula:
SE = sqrt((SD1^2 / n1) + (SD2^2 / n2))
Where:
- SD1 and SD2 are the standard deviations of the two samples
- n1 and n2 are the sample sizes of the two samples
In this case, SD1 = $2200, SD2 = $2800, n1 = n2 = 50.
SE = sqrt((2200^2 / 50) + (2800^2 / 50))
Step 2: Calculate the margin of error.
The margin of error is determined using the z-score corresponding to the desired confidence level. For a 95% confidence level, the z-score is approximately 1.96.
Margin of Error = z * SE
In this case, z = 1.96 (for a 95% confidence interval).
Margin of Error = 1.96 * SE
Step 3: Calculate the confidence interval.
The confidence interval is calculated by subtracting and adding the margin of error from the difference in sample means.
Confidence Interval = (sample mean 1 - sample mean 2) ± Margin of Error
In this case, sample mean 1 = $44600, sample mean 2 = $43800.
Confidence Interval = ($44600 - $43800) ± Margin of Error
Now you can plug in the values to calculate the confidence interval.