Tonya wants to estimate what proportion of the students in her dormitory like the dorm food. She interviews an SRS of 50 of the 175 students living in the dormitory. She finds that 14 think the dorm food is good.
a.) What population does Tonya want to draw conclusions about?
b.) In your own words, what is the population proportion (p) in this setting?
c.) What is the numerical value of the sample proportion (^P) from Tonya's sample?
Please help! Thanks!
a. All students in her dorm
b. I'm not sure what you are asking. The sample is 50/175 of the population.
c. Again, I'm not sure what you are asking. Are you referring to 14/50?
a) Tonya wants to draw conclusions about the population of all students living in her dormitory.
b) In this setting, the population proportion (p) would represent the proportion of all students living in the dormitory who like the dorm food.
c) The numerical value of the sample proportion (^P) from Tonya's sample is 14/50, which is approximately 0.28 or 28%.
a.) Tonya wants to draw conclusions about the students living in her dormitory. The population of interest is the 175 students who live in the dormitory.
b.) In this setting, the population proportion (p) refers to the proportion of all the students in the dormitory who like the dorm food. It represents the true percentage or proportion of students who have a positive opinion about the food.
c.) To find the numerical value of the sample proportion (^P), we take the number of students in the sample who think the dorm food is good (14) and divide it by the total number of students in the sample (50).
So, ^P = 14/50 = 0.28.
Therefore, Tonya's sample proportion is 0.28 (or 28%). This means that out of the students in her sample, 28% think the dorm food is good.