Question

Suppose that a student in this class uses their personalized class data set to find the following confidence interval for the proportion of students in this class who travel more than 5 km to school: (.171, .243). Consider the following statements.

(i) The proportion of students in that same student's personalized class data set who travel more than 5km to school might not be in the interval (.171, .243).

(ii) The true proportion of students in this class who travel more than 5km to school must be in the interval (.171, .243).

(iii) If that same student used the same data set to produce the following confidence interval for the proportion of students who travel more than 5km to school, (.184, .230), then this new confidence interval must have a lower level of confidence than the interval (.171, .243).

Determine which of the above statements are true (1) or false (2).

Answer 1

(i) The proportion of students in that same student's personalized class data set who travel more than 5km to school might not be in the interval (.171, .243).

FALSE

(ii) The true proportion of students in this class who travel more than 5km to school must be in the interval (.171, .243).

TRUE

(iii) If that same student used the same data set to produce the following confidence interval for the proportion of students who travel more than 5km to school, (.184, .230), then this new confidence interval must have a lower level of confidence than the interval (.171, .243).

TRUE