Question

Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p. nequals=​130, xequals=​69; ​90% confidence

Answer 1

Solution :

n = 130

x = 69

= x / n = 69 / 130 = 0.531

1 - = 1 - 0.531 = 0.469

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 * (((0.531 * 0.469) / 130 )

= 0.072

A 90 % confidence interval for population proportion p is ,

- E < P < + E

0.531 - 0.072 < p < 0.531 + 0.072

0.459 < p < 0.603