Question

Stephan makes 19 out of 25 foul shots. Use the normal distribution in probability and confidence interval calculations.

1. a) What is the a value for a confidence level of 80%?

2. b) What is the standard deviation of the sample proportion x/n where x is the number

   of made shots and n is the total number of shots?

3. c) What is the 80% confidence interval for underlying average foul shot percentage?

Answer 1

Solution :

Given that,

a) At 80% confidence level

= 1 - 80%

=1 - 0.80 =0.20

/2 = 0.10

Z/2 = Z_{0.10 = 1.282}

b) n = 25

x = 19

Point estimate = sample proportion = = x / n = 19 / 25 = 0.76

1 - = 1 - 0.76 = 0.24

=  [p ( 1 - p ) / n] = [(0.76 * 0.24) / 25 ] = 0.0854

Margin of error = E = Z _{/ 2} *

= 1.96 * 0.0854

= 0.109

c) A 80% confidence interval for population proportion p is ,

± E  

= 0.76  ± 0.109

= ( 0.651, 0.869 )