Question

A university planner wants to determine the proportion of spring semester students who will attend summer school. She surveys 35 current students discovering that 15 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 = 35

x = 15

Point estimate = sample proportion = = x / n = 15/35=0.429

1 - = 1 - 0.429=0.571

At 90% confidence level

= 1 - 90%

=1 - 0.90 =0.10

=0.10
Z=Z0.10=1.28

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

= 1.28 (((0.429*0.571) /35 )

= 0.1071

A 90% confidence interval for population proportion p is ,

- E

0.429 - 0.1071  

0.3219

lower bound =0.3219