Algebra 2 - Sample Size

Question

Of 1000 patients currently admitted at Bey Area Hospital, 300 participate in a survey. The patients are asked whether they are, or are not, satisfied with the quality of care they receive from hospital staff. A total of 207 patients indicate they are satisfied with their quality of care.

Part A: Based on this information, how many patients in the hospital are likely not satisfied with their quality of care?

Part B: Assuming a 95% confidence level, determine the approximate margin of error for this study.

Answer 1

Part A:

Let like = 0 and don't like = 1

x^bar = (0(207) + 1(93))/300 = 0.31

x^bar(population) = 0.31(1000) = 310 people are not satisfied with their quality of care

Part B: To find the margin of error for 95% confidence, need to find the sample standard deviation, S.

σ_x-bar = σ/√samplesize = σ/√300 ≈ S/17.3

S² = (207(0-.31)² + 93(1-0.31)²)/299 = 0.28 --> S = 0.53

S/17.3 = 0.53/17.3 = 0.03

2 Margins of error = ±0.06

Answer 2

Part A : Roughly, 700 patients are not satisfied with the quality of their care in the hospital.

Part B:2 margins