A computer repair service found that a random sample of 45 repair costs had a mean cost of $659. Assume that the population standard deviation is $125. Calculate the margin of error, E, for a 95% confidence interval for the population mean µ.
95% = mean ± 1.96 SEm
SEm = SD/√n
I'll let you do the calculations.
To calculate the margin of error (E) for a 95% confidence interval for the population mean (µ), you can use the following formula:
E = z * (σ / √n)
Where:
- E is the margin of error
- z is the z-score corresponding to the desired confidence level (95% confidence level corresponds to a z-score of 1.96)
- σ is the population standard deviation
- n is the sample size
In this case, the sample size (n) is 45 and the population standard deviation (σ) is $125. Therefore, we can substitute these values into the formula:
E = 1.96 * (125 / √45)≈ 1.96 * (125 / 6.708203932) ≈ 1.96 * 18.64800338 ≈ 36.51503043
So, the margin of error for a 95% confidence interval is approximately $36.52.