Question

Assuming that the population is normally​ distributed, construct a 90% confidence interval for the population​ mean, based on the following sample size of n=7.

​1, 2,​ 3, 4, 5 6, and 24

Change the number 24 to 7 and recalculate the confidence interval. Using these​ results, describe the effect of an outlier​ (that is, an extreme​ value) on the confidence interval.

Answer 1

(a)

From the given data, the following statistics are calculated:

n = 7

= Sample Mean = 45/7 = 6.4286

s = Sample SD = 7.9343

SE = s/

= 7.9343/ = 2.9989

df = n - 1 = 7 - 1 = 6

= 0.10

From Table, critical values of t = 1.9432

Confidence Interval:

6.4286 (1.9432 X 2.9989)

= 6.4286 5.8274

= ( 0.6012,12.2560)

So,

Confidence Interval is given by:

0.6012 < < 12.2560

(b)

Changing the number 24 to 7, we get:

From the given data, the following statistics are calculated:

n = 7

= Sample Mean = 28/7 = 4

s = Sample SD = 2.1602

SE = s/

= 2.1602/ = 0.8165

df = n - 1 = 7 - 1 = 6

= 0.10

From Table, critical values of t = 1.9432

Confidence Interval:

4 (1.9432 X 0.8165)

= 4 1.5866

= (2.4134,5.5866)

So,

Confidence Interval is given by:

2.4134 < < 5.5866

(c)

The width of the confidence level decreases if outlier is removed from the data set.