Question

Title: At the 99% confidence level, what is the proportion of teenagers who play tennis?

____ 3.- Out of a sample of 120 teenagers, 14 of them responded YES to the question “Do you play tennis?” To answer the question in the title:

We would calculate a confidence interval centered at p_hat with a margin of error of 2.576*sqrt(0.12*(1-0.12)/120).

We would calculate a confidence interval centered at p with a margin of error of 2.576*sqrt(0.12*(1-0.12)/120).

We would calculate a significance test with z=sqrt(0.12*(1-0.12)/120).

We would calculate a significance test with Ho: p_hat=0.12.

Both c and d.

Answer 1

Solution :

Given that,

n = 120

x = 14

= x / n = 14 / 120 = 0.117

1 - = 1 - 0.117 = 0.883

At 99% confidence level the z is ,

= 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

Z_/2 = Z_0.005 = 2.576

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

= 2.576 * ((0.117 * 0.883) / 120)

= 0.076

A 99% confidence interval for population proportion p is ,

- E < P < + E

0.117 - 0.076 < p < 0.117 + 0.076

0.041 < p < 0.192

The 95% confidence interval for the population proportion p is : (0.041 , 0.192)