Question

x

5.016034258

6.264669973

7.010906671

6.812848737

7.850341763

8.838969458

5.145890441

8.220602848

5.277426227

4.05011136

5.234050643

7.473562449

4.985357776

10.59658286

5.904335683

7.753961794

4.892876349

6.144314278

8.497047406

5.978487605

3.833994369

5.785603653

10.01757147

5.387738603

7.01690057

5.796890442

5.818420646

There are 27 independently drawn random observations on a variable X. It is known that σ^2=3.12

1. Construct a 95% confidence interval for E(X). Show your working.
2. Interpret the confidence interval.
3. Do you need to make any assumptions in order for your confidence interval to be valid?

Answer 1

Since, the sample size is 27, which is less than 30 the distribution is considered following t-distribution.

The degree of freedom = n-1=26

The sample mean = 6.503907

The variance = σ^2=3.12

The level of significance = 5%

The confidence interval is given by upper and lower limit.

Thus, the 95% confidence interval for E(x) is:

5.805002 <= E(x)<= 7.202813

For this confidence interval to be valid, it is assumed that the 27 values are continuous distribution and follows t-distribution.