Question

Of 41 bank customers depositing a check, 15 received some cash back. (a) Construct a 90 percent confidence interval for the proportion of all depositors who ask for cash back. (Round your answers to 4 decimal places.) The 90% confidence interval is from () to ()

Answer 1

Solution :

n = 41

x = 15

= x / n = 15 / 41 = 0.3659

1 - = 1 - 0.3659 = 0.6341

At 90% confidence level the z is ,

= 1 - 90% = 1 - 0.90 = 0.10

/ 2 = 0.10 / 2 = 0.05

Z_/2 = Z_0.05 = 1.645

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

= 1.645 * (((0.3659 * 0.6341) /41)

= 0.1237

A 90 % confidence interval for population proportion p is ,

- E < P < + E

0.3659 - 0.1237 < p < 0.3659 + 0.1237

0.2422< p < 0.4896