Question

A university planner wants to determine the proportion of spring semester students who will attend summer school. She surveys 32 current students discovering that 17 will return for summer school. At 90% confidence, compute the lower bound of the interval estimate for this proportion.

Answer 1

Solution :

Given that,

n = 32

x = 17

Point estimate = sample proportion = = x / n = 17 /32=0.531

1 - = 1 - 0.531=0.469

At 90% confidence level

= 1 - 90%  

= 1 - 0.90 =0.10

=0.10

Z = Z_{0.10 =1.28}

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

=1.28 (((0.531*0.469) /32 )

E = 0.1129

A 90% confidence interval for population proportion p is ,

- E

0.531 - 0.1129

0.4181

lower bound = 0.4181