Question

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.

Answer 1

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