Question

Data on pull-off force (pounds) for connectors used in an automobile engine application are as follows:

79.7	75.1	78.2	74.1	73.9	75.0	77.6	77.3	73.8	74.6	75.5	74.0	74.7
75.9	72.8	73.8	74.2	78.1	75.4	76.3	75.3	76.2	74.9	78.0	75.1	76.8

If necessary, round all intermediate calculations to four decimal places (e.g. 12.3456).
(a) Calculate a point estimate of the mean pull-off force of all connectors in the population (Round the answer to four decimal places (e.g. 90.2353).)

(b) Calculate a point estimate of the pull-off force value that separates the weakest 50% of the connectors in the population from the strongest 50% (Express the answer to two decimal place (e.g. 90.15).)

(c) Calculate the point estimate of the population variance (Round the answer to three decimal places (e.g. 3.567).)

(d) Calculate the point estimate of the population standard deviation (Round the answer to two decimal places (e.g. 1.23).)

(e) Calculate the standard error of the point estimate found in part (a) (Round the answer to two decimal places (e.g. 1.23).)

(f) Calculate a point estimate of the proportion of all connectors in the population whose pull-off force is less than 73 pounds (Round the answer to three decimal places (e.g. 0.123).)

Answer 1

putting above data in ascending order:

x
72.8
73.8
73.8
73.9
74
74.1
74.2
74.6
74.7
74.9
75
75.1
75.1
75.3
75.4
75.5
75.9
76.2
76.3
76.8
77.3
77.6
78
78.1
78.2
79.7

a)\

point estimate of the mean =total/n =

75.6269

b)

point estimate of the median =middle value =(75.1+75.3)/2 =

75.2

c)

point estimate of the population variance s^2=

2.8844

d)

point estimate of the population standard deviation s =1.6984

e)

standard error of the point estimate =std deviation/√n=0.3331

f)

point estimate of the proportion of all connectors in the population whose pull-off force is less than 73 pounds =1/26 = 0.04