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

(ii) 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 higher level of confidence than the interval (.171, .243).

(iii) 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).

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

Answer 1

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

True

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

False

Width of new confidence interval = 0.230 - 0.184 = 0.046

Width of old confidence interval = 0.243 - 0.171 = 0.072

Here width of new confidence interval is less than old confidence interval

In general, width of confidence interval increases as confidence level increases.

iii) 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