Question

5. A random sample of 90 bicycle-riding adults in NY indicate that 60 always wore a hemit while riding.
Use the sample information to develop a 90% confidence interval estimate for the true population proportion
of bicycle-riding adults in NY who wear a helmet while riding.

Answer 1

Solution :

n = 90

x = 60

= x / n = 60 / 90 = 0.667

1 - = 1 - 0.667 = 0.333

At 90% confidence level the z is ,

= 1 - 90% = 1 - 0.90 = 0.10

/ 2 = 0.10 / 2 = 0.05

Z/2 = Z0.05 = 1.645

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

= 1.645 * (((0.667 * 0.333) / 900)

= 0.082

A 90 % confidence interval for population proportion p is ,

- E < P < + E

0.667 - 0.082 < p < 0.667 + 0.082

0.585 < p < 0.749