Question

The Accompanying data describe flexural strength (Mpa) for concrete beams of a certain type as shown in below.

     9.2         9.7         8.8         10.7       8.4         8.7         10.7

                             6.9         8.2         8.3         7.3         9.1         7.8         8.0

                             8.6         7.8         7.5         8.0         7.3         8.9         10.0

                             8.8         8.7         12.6       12.3       12.8       11.7

6-b. Calculate and interpret a point estimate of the population standard deviation.

6-c. Calculate a point estimate of the proportion of all such beams whose flexural strength exceeds 11 Mpa

6-d. Calculate a point estimate of the population coefficient of variation.

Answer 1

1)

X	(X - X̄)²
9.2	0.00
9.7	0.31
8.8	0.12
10.7	2.43
8.4	0.55
8.7	0.19
10.7	2.431
6.9	5.021
8.2	0.885
8.3	0.707
7.3	3.388
9.1	0.002
7.8	1.798
8	1.301
8.6	0.292
7.8	1.798
7.5	2.692
8	1.301
7.3	3.388
8.9	0.058
10	0.738
8.8	0.116
8.7	0.194
12.6	11.966
12.3	9.981
12.8	13.3902
11.7	6.5498

	X	(X - X̄)²
total sum	246.8	71.61
n	27	27

Point estimate Population std dev =   √ [ Σ(X - X̄)²/(n-1)] =   √   (71.6052/26)   =       1.6595

2)

Number of Items of Interest,   x =   4
Sample Size,   n =    27
      
Sample Proportion ,    p̂ = x/n =    0.1481

3)

mean =    ΣX/n =    246.800   /   27   =   9.1407

coefficient of variation = S.D / Mean * 100

= 1.6595 / 9.1407

= 0.181550647 * 100

= 18.16 %

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