Question

# Explain how an interval estimate is more informative than a point estimate by solving the...

Explain how an interval estimate is more informative than a point estimate by solving the following, providing the TI commands, and comparing the two. When asked if marriage is becoming obsolete, 782 out of 2004 randomly selected adults who responded to a 2010 Pew Poll said yes. Find the point estimate for the percentage of adults who said yes, then find a 95% confidence interval for the proportion of adults who said yes.

Solution :

Given that,

n = 2004

x = 782

Point estimate = sample proportion = = x / n = 782 / 2004 = 0.390

1 - = 1 - 0.390 = 0.610

At 95% confidence level

= 1 - 95%

=1 - 0.95 =0.05

/2 = 0.025

Z/2 = Z0.025 = 1.960

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

= 1.96 (((0.390 * 0.610) / 2004)

= 0.021

A 95% confidence interval for population proportion p is ,

± E

= 0.390  ± 0.021

= ( 0.369, 0.411 )

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