Question

Confidence Intervals and Minimum Sample Sizes Use your set of z-scores to find the following:

11. Out of 54 randomly selected patients of a local hospital who were surveyed, 49 reported that they were satisfied with the care they had received.

Construct a 95% confidence interval for the percentage of patients satisfied with their care at the hospital.

Answer 1

Solution :

Given that,

n = 54

x = 49

Point estimate = sample proportion = = x / n = 49/54=0.907

1 -   = 1- 0.907 =0.093

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.96   ( Using z table )

Margin of error = E = Z/2   * ((( * (1 - )) / n)

= 1.96 (((0.907*0.093) / 54)

E = 0.077

A 95% confidence interval proportion p is ,

- E < p < + E

0.907-0.077 < p < 0.907+0.077

0.830< p < 0.984

(0.830 , 0.984)