Question

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

79.3  75.1  78.2  74.1  73.9  75.0  77.6  77.3  73.8  74.6  75.5  74.0  74.7

75.97  2.9   73.8  74.2  78.1  75.4  76.3  75.3  76.2  74.9  78.0  75.1  76.8

a. Calculate a point estimate of the mean pull-off force of all connectors in the population. State which estimator you used and why.

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%.

c. Calculate point estimates of the population variance and the population standard deviation.

d. Calculate the standard error of the point estimate found in part (a). Interpret the standard error.

e. Calculate a point estimate of the proportion of all connectors in the population whose pulloff force is less than 73 pounds.

Answer 1

Solution

a. Calculate a point estimate of the mean pull-off force of all connectors in the population. State which estimator you used and why.

By the formula:

                                     

Then 

                                     

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%.

By the formula:

                                         

Since: 𝑛=26

Then:  

                                         

While: x₁₃=75.1 and x₁₄=75.3

So, that:

                                         

c. Calculate point estimates of the population variance and the population standard deviation.

Where 𝑆 is standard deviation

          𝑆² is variance:

By the formula:

                                   

While 𝑛=26

Therefore:     S=2.74

d. Calculate the standard error of the point estimate found in part (a). Interpret the standard error

By the formula:

                                     

Since: 𝑆=1.65 and 𝑛=26

Then:

                                       

e. Calculate a point estimate of the proportion of all connectors in the population whose pull-off force is less than 73 pounds.

By formula:

                         

Then: