Question

In a random sample of 400 registered voters, 144 indicated they plan to vote for Candidate A.

Determine a 95% confidence interval for the proportion of all the registered voters who will vote for Candidate A.

Value from the appropriate table=

Margin of error=

Lower limit of C.I.=

Upper limit of C.I.=

Answer #1

**n = 400**

**
= proportion of registered voters who vote A**

**
= 144/400**

**
= 0.36**

**Margin of error = critical
value
SE**

**SE = [(1-
)/n] ^{1/2} **

**= [0.36(1 -
0.36)/400] ^{1/2} **

**= 0.024**

**Margin of error =
1.96
0.024**

**=
0.04704**

**95% confidence interval is
given by**

**
+/- 1.96 [(1-
)/n] ^{1/2} **

**0.36 +/-
1.96(0.024)**

**0.36 +/-
0.04704**

**0.36 - 0.04704, 0.36 +
0.04704**

**0.31296 ,
0.40704**

**confidence interval
is [0.31296 , 0.40704 ]**

**lower limit =
0.31296**

**upper limit =
0.40704**

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