Of 100 randomly selected people in Oregon, 45 said they were going to vote yes on...

Of 100 randomly selected people in Oregon, 45 said they were going to vote yes on Proposition 1.

Construct a 95% confidence interval and round answers to 3 decimal places _____,____ (i.e. 0.123)

Expert Solution

Level of Significance,   α =    0.05
Number of Items of Interest,   x =   45
Sample Size,   n =    100

Sample Proportion ,    p̂ = x/n =    0.450
z -value =   Zα/2 =    1.960   [excel formula =NORMSINV(α/2)]

Standard Error ,    SE = √[p̂(1-p̂)/n] =    0.0497
margin of error , E = Z*SE =    1.960   *   0.0497   =   0.0975

95%   Confidence Interval is
Interval Lower Limit = p̂ - E =    0.450   -   0.0975   =   0.3525
Interval Upper Limit = p̂ + E =   0.450   +   0.0975   =   0.5475

so, confidence interval is (   0.352   < p <    0.548   )

orchestra answered 2 years ago

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