Question

During the last smeater , 60 students of planning and public policy program (PPPP) at rutgers university took the basic statistic course, Twelve of these stjdents received more than 80 for the final exam. At 99% level of confidence, estimate the percentage of all students of PPPP who recieved more than 80 for the final exam of the badic statistics course during the last 10 years

During the last semester, 60 students of Planning and Public Policy Program (PPPP) at Rutgers University took the Basic Statistics course. Twelve of these students received more than 80 for the final exam. At 99% level of confidence, estimate the percentage of all students of PPPP who received more than 80 for the final exam of the Basic Statistics course during the last 10 years. 7% to 33% 18% to 22% 59% None of the above

Answer 1

Solution:

The 99% confidence interval for population percentage is given as follows:

pg (p = Zoo Vn

Where, p̂ is sample percentage, q̂ = 100 - p̂, n is sample size and Z_(0.01/2) is critical z-value to construct 99% confidence interval.

Sample percentage of students of PPPP who received more than 80 for the final exam is, p̂ = (12/60)×100 = 20%

q̂ = 100 - 20 = 80% and n = 60

Using Z-table we get, Z_(0.01/2) = 2.58

Hence, 99% confidence interval to estimate the percentage of all students of PPPP who received more than 80 for the final exam of the basic statistics course during the last 10 years is,

20 x 80 20+ 2.58 x V 60

= (20+13.32)

= (20-13.32.20+13.32)

= (6.68, 33.32)

On rounding to nearest integer we get, confidence interval as

(7.33)

Hence, 99% confidence interval estimate of the percentage of all students of PPPP who received more than 80 for the final exam of the basic statistics course during the last 10 years is, 7% to 33%.

Please rate the answer. Thank you.