Answer:
Correct option: (c) Paired samples t confidence interval.
Step-by-step explanation:
A paired data is collected from an experiment that is conducted twice; once before applying a treatment and second time after the treatment has been applied.
For example, scores of students before the coaching classes and after the coaching classes.
In this case a paired data is collected.
The runners were asked to run 100-yard wearing their usual shoes one day and do same thing the next day wearing the company's shoes.
The two data collected from both the days is a paired data.
To determine whether the salesman's claim that the runners would run faster races if they wore the company's brand of running shoe is correct or not a confidence interval can be constructed for the paired the data.
If the true mean difference is contained in the interval then the salesman's claim can be considered true otherwise false.
To construct this confidence interval use a paired sample t confidence interval.
Because the population standard deviations are not known.
The (1 - <em>α</em>)% confidence interval for the paired difference is: