3. An automotive supplier of interior parts places several electrical wires in a

Question

3. An automotive supplier of interior parts places several electrical wires in a harness. A pull test measures the force required to pull spliced wires apart. Let X equal the force required to pull spliced wires apart. Assume that the distribution of X is N(, 2). The following data give 20 observations of X : 28.8 24.4 30.1 25.6 26.4 23.9 22.1 22.5 27.6 28.1 20.8 27.7 24.4 25.1 24.6 26.3 28.2 22.2 26.3 24.4

a. Find and interpret 95% confidence interval for the true mean force required to pull the spliced wires apart.

b. A customer requires that wires withstand a pull force of 20 pounds. Based on your findings in part (a) will the customer be satisfied? Explain.

For part a) I got the CI to be between 24.31 and 26.64.

b) I would assume that the customer would not be satisfied as 20 pounds falls outside the range of the 95% CI. But, I really don't have an explaination for this. It would be great that someone could explain this to me.

Thank you for any help :)

Explanation / Answer

The 95% confidence interval quantifies the random error associated with our estimate, and it can also be interpreted as the range within which the true value is likely to lie with 95% confidence. This means that values outside the 95% confidence interval are unlikely to be the true value. Therefore, if the null value (20) is not contained within the 95% confidence interval, then the probability that the null is the true value is less than 5%. Conversely, if the null is contained within the 95% confidence interval, then the null is one of the values that is consistent with the observed data.

thus we can say that if any data point here 20 lies outside the confidence interval which is not outlier as well then the data point then it lies only in rejection region ,thus it implies customer will not get satisfy.

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