A simple random sample of size n=250 individuals who are currently employed is asked if they work at home at least once per week. Of the 250 employed individuals surveyed, 31 responded that they did work at home at least once per week. Construct a 99% confidence interval for the population proportion of employed individuals who work at home at least once per week.
(a) The lower bound is __ and the upper bound is __.
Sample proportion = 31 / 250
= 0.124
99% confidence interval for p is
-
Z
/2 * sqrt [
( 1 -
) / n ] <
p <
+
Z
/2 * sqrt [
( 1 -
) / n ]
0.124 - 2.576 * sqrt [ 0.124 ( 1 - 0.124) / 250 ] < p < 0.124 + 2.576 * sqrt [ 0.124 ( 1 - 0.124) / 250 ]
0.070 < p < 0.178
99% CI is ( 0.070 , 0.178 )
The lower bound is 0.070 and the upper bound is 0.178
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