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, 75.9, 72.9, 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 pull-off force is less than 73 pounds

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Step-by-step explanation:

Given the data:

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, 75.9, 72.9, 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.

The mean can be used as a point estimate for the pull of force.

Using a calculator :

The mean(m) :

Σx /n = 1966/26

= 75.62 pounds

(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%.

To obtain this, we calculate the median:

Median = 0.5(n + 1)th term

Median = 0.5(27)th term = 13.5

Take the 13th and 14th term:

(75.1 + 75.3) / 2 = 75.2 pounds

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

Using calculator ; the variance (s²) = 2.73815

The standard deviation (s) = √variance

s = √2.73815 = 1.655

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

Standard Error = standard deviation / √n

Standard Error = 1.655 / √26

= 0.3245

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

Number of Proportions less than 73 pounds / number of samples

= 1 / 26

= 0.0385