Question

Suppose you work for Fender Guitar Company and you are responsible for testing the integrity of...

Suppose you work for Fender Guitar Company and you are responsible for testing the integrity of a new formulation of guitar strings. To perform your analysis, you randomly select 52 'high E' strings and put them into a machine that simulates string plucking thousands of times per minute. You record the number of plucks each string takes before failure and compile a dataset. You find that the average number of plucks is 6,143.3 with a standard deviation of 266.95. A 90% confidence interval for the average number of plucks to failure is (6,081.3, 6,205.3). From the option listed below, what is the appropriate interpretation of this interval? Question 2 options:

1) We are certain that 90% of the average number of plucks to failure for all 'high E' strings will be between 6,081.3 and 6,205.3.

2) We are 90% confident that the average number of plucks to failure for all 'high E' strings is between 6,081.3 and 6,205.3.

3) We are 90% confident that the proportion of all 'high E' guitar strings fail with a rate between 6,081.3 and 6,205.3.

4) We cannot determine the proper interpretation of this interval.

5) We are 90% confident that the average number of plucks to failure for all 'high E' strings tested is between 6,081.3 and 6,205.3.

option 1, 3, 4 and 5 are incorrect option 1 is including "certain" which is incorrect for confidence interval, option 3 is using the "proportion" which is also incorrect, option 4 is showing incorrect statement and option 5 is incorrect because it is showing us that we are able to find the 90% confidence interval only for the tested strings, so it is also incorrect.

only option 2 is correct answer because this statement is correct, i.e. we are 90% confident that the average number of plucks to failure for all High E strings is between 6081.3 and 6205.3.

So, answer is option 2

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