21.4 A student survey. 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.
What is your question?
(175-14)/175 = proportion who do not think that dorm food is bad, which is not necessarily the same as saying it is good.
92
To estimate the proportion of students in the dormitory who like the dorm food, Tonya can use the information from her sample survey. Let's go through the steps to calculate the estimated proportion.
Step 1: Identify the sample size and the number of students who like the dorm food.
- Sample size (n): 50
- Students who like the dorm food (x): 14
Step 2: Calculate the estimated proportion.
The estimated proportion (p̂) can be calculated by dividing the number of students who like the dorm food by the sample size.
- p̂ = x / n
- p̂ = 14 / 50
- p̂ = 0.28 (rounded to two decimal places)
Step 3: Interpret the result.
According to the sample survey, an estimated proportion of 0.28 (or 28%) of the students in the dormitory like the dorm food.
It's important to note that this is just an estimate based on the sample survey, and the true proportion in the entire dormitory population may vary.