Question

Researchers report that 14 of 38 patients (37%) interviewed cited lack of respect by the health-care system as a reason for failing to keep doctor's appointments in the past. Specifically, being kept waiting for an appointment, in the waiting room, and in the exam room were taken as evidence of insufficient respect.

a) Produce a 95% confidence interval for the proportion of all patients who miss appointments because of perceived lack of respect. (Round your answers to three decimal places.)

Answer 1

Solution :

Given that,

n = 38

x = 14

Point estimate = sample proportion = = x / n = 14 / 38 = 0.37

1 - = 1 - 0.37 = 0.63

At 95% confidence level

= 1 - 95%

=1 - 0.95 =0.05

/2 = 0.025

Z/2 = Z0.025 = 1.960

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

= 1.96 (((0.37 * 0.63) /38 )

= 0.154

A 95% confidence interval for population proportion p is ,

± E   

= 0.37  ± 0.154

= ( 0.216, 0.524 )