Question

The random sample shown below was selected from a normal distribution.

5,

6​,

10​,

7​,

5​,

3

  

Complete parts a and b.

a. Construct a 90​% confidence interval for the population mean μ.

Answer 1

From the data given , we get

Sample mean ,

Sample standard deviation is computed as follows :

data	data-mean	(data - mean)2
5	-1	1
6	0	0
10	4	16
7	1	1
5	-1	1
3	-3	9
Total		28

Sample size , n =6

Significance level , = 0.1

Degrees of freedom, df = n-1 = 6-1 = 5

The critical value for α=0.1 and  df is t_c​​=2.015.

The corresponding 90% confidence interval for the population mean μ is computed as shown below: