Question

4. I sample 200 PCC students to see whether or not they drink coffee at school, and find the confidence interval for the proportion who say they do drink coffee to be (0.65, 0.78) at the 95% confidence level. For the statements below, determine if they are True or False. Make your responses clear and legible!

A. 95% of all students drink coffee between 65% and 78% of the time.

B. We’re 95% confident that the students sampled drink coffee between 65% and 78% of the time.

C. 147 of the students sampled said they drink coffee at school.

D. Between 65% and 78% of the students drink 95% of all the coffee drank at school.

E. 143 of the students sampled said they drink coffee at school.

F. We’re 95% confident that the true proportion of PCC students who drink coffee at school is between 65% and 78%.

G. We’re 95% confident that the interval between 65% and 78% has captured the true proportion of PCC students who drink coffee at school.

H. We’re between 65% and 78% confident that the true proportion of PCC students who drink coffee is 95%.

Answer 1

Answer:

Given that:

I sample 200 PCC students to see whether or not they drink coffee at school, and find the confidence interval for the proportion who say they do drink coffee to be (0.65, 0.78) at the 95% confidence level.

A) 95% of all students drink coffee between 65% and 78% of the time.

False (since interval is for population proportion and not individuals)

B) We’re 95% confident that the students sampled drink coffee between 65% and 78% of the time.

False

C) 147 of the students sampled said they drink coffee at school.

False (since sample proportion =(0.65+0.78)/2 =0.715 , therefore number of people =200*0.715=143)

D) Between 65% and 78% of the students drink 95% of all the coffee drank at school.

False

E) 143 of the students sampled said they drink coffee at school.

True

F) We’re 95% confident that the true proportion of BBC students who drink coffee at school is between 65% and 78%

True

G) We’re 95% confident that the interval between 65% and 78% has captured the true proportion of PCC students who drink coffee at school

True

H)  We’re between 65% and 78% confident that the true proportion of PCC students who drink coffee is 95%.

False