Confidence Interval Margin of Error Calculation
The question asks for the margin of error component of the 95% confidence interval for the mean. We are given:
- Sample size, $n = 16$
- Sample mean, $\bar{x} = 40$
- Standard deviation, $sd = 4.0$
- Z-score for 95% confidence, $Z = 1.96$
Calculating the Margin of Error (ME)
The formula to calculate the margin of error for a population mean using a Z-distribution is:
$ ME = Z \times \frac{sd}{\sqrt{n}} $
Substitute the given values into the formula:
- Calculate the standard error of the mean (SEM):
$ SEM = \frac{sd}{\sqrt{n}} = \frac{4.0}{\sqrt{16}} = \frac{4.0}{4} = 1.0 $
- Calculate the margin of error:
$ ME = Z \times SEM = 1.96 \times 1.0 = 1.96 $
The margin of error is $1.96$. Therefore, the 95% confidence interval is typically expressed as $\bar{x} \pm ME$, which would be $40 \pm 1.96$. The value representing the interval's range around the mean is $\pm 1.96$.
Important Questions from Statistical estimation
Calculate the median using the following data.
Lower class boundary of the median class = 40
Total frequency = 120
Frequency of the median class = 35
Less than cumulative frequency of the post median class = 37
Class width = 20
The ______ is an unbiased estimator of the population mean.
If xi = i / 5 + 2, where i = 1, 2,..., 5, then the mean of x1, x2, ..., x5 is:
How many employees get salaries less than Rs 30,000?
Salary Data of Employees in a Company
The following data shows salaries of all the employees of a company:
Salary (in Rs.) / वेतन (रुपये में) 0 - 10,000 10,001 - 20,000 20,001 - 30,000 30,001 - 40,000 40,001 - 50,000 Number of Employees / कर्मचारियों की संख्या 235 105 50 40 20 Calculate the standard deviation if the mean of a certain set of observations is 20 and the mean of the squares of the same observations is 500.
