For a given month, a random sample of 30 sales girls from a superstore has a sample mean of salary of RM 800 with standard deviations of RM 140. Estimate the mean monthly salary for all employees using the 95% confidence interval.(what does mean of 95% confidence level?)
sales GIRLS?
I didn't know any store hired children!
95% confidence interval = mean ± 1.96 SEm
SEm = SD/√n
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A 95% confidence level indicates that if we were to repeat this sampling process multiple times, approximately 95% of the computed confidence intervals would contain the true population mean. In other words, there is a 95% probability that the interval we calculate will capture the true population mean.
To estimate the mean monthly salary for all employees using the 95% confidence interval, we can use the formula:
Confidence Interval (CI) = Sample mean +/- Margin of Error,
where the Margin of Error can be calculated using the formula:
Margin of Error = Critical value * Standard deviation / Square root of sample size.
To find the critical value, we need to refer to the Z-table or use a statistical calculator. For a 95% confidence level, the critical value is approximately 1.96 (assuming a large sample size).
Now, let's calculate the confidence interval:
CI = Sample mean +/- Margin of Error
= 800 +/- (1.96 * 140 / √30)
First, calculate the margin of error:
Margin of Error = 1.96 * 140 / √30
≈ 81.17
Now, substitute the margin of error back into the confidence interval formula:
CI = 800 +/- 81.17
= (718.83, 881.17)
Therefore, with a 95% confidence level, we can estimate that the mean monthly salary for all employees lies between RM 718.83 and RM 881.17.