Question

Illustrate a Systematic Sample of a population. Calculate the required descriptive statistics. Create a sample composed of at least 9 values. Determine a 95% Confidence Interval of the Mean. Use in an excel spreadsheet.

Answer 1

Answer to the question)

In excel , in cell A1 , type:

=randbetween(0,10)

this generates random number between 0 to 10

drag this command to next 50 cells

Like this we get 50 random numbers in excel

.

Now to form a systematic sample, let the strategy be to select every 5th number in the sample

.

Like this we get the following sample:

.

Sample size ( n) = 10

In any vacant cell type the formula:

=average(c1:c10)

[in cells c1 to c10 we have the 10 values of the sample]

[this command gives the value of sample mean x bar]

x bar = 5.6

.

Likewsie use =stdev(c1:c10) to get the value of standard deviation s

s = 2.72

.

T value for 95% confidence level and df = n - 1 = 9 can be obtained from the t table:

.

t = 2.262

.

The formula of confidence interval is:

Lower interval = xbar - t * s / sqrt(n)

Upper interval = x bar + t * s/ sqrt(n)

.

On plugging the values we get:

Lower interval = 5.6 - 2.262 * 2.72 / sqrt(10) = 3.6544

Upper interval = 5.6 + 2.262 * 2.72 / sqrt(10) = 7.5456

.

Thus the 95% confidence interval of sample mean is: (3.6544 , 7.5456)