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Chauncey determined that 50 percent of students at his school voted Republican in the last election, with a sampling error (also known as standard error) of 5 percent. What is the confidence interval for 95 percent confidence level?

Respuesta :

Answer:

95% confidence interval: (0.402,0.598)

Step-by-step explanation:

We are given the following in the question:

Proportion of student who voted Republican in the last election = 50%

[tex]\hat{p} = 50\% = 0.5[/tex]

Standard error = 5% = 0.05

95% confidence interval:

[tex]\hat{p}\pm z_{stat}\times (\text{Standard error})[/tex]

[tex]z_{critical}\text{ at}~\alpha_{0.05} = 1.96[/tex]

Putting values, we get,

[tex]=0.5 \pm (1.96)(0.05)\\=0.5\pm 0.098\\=(0.402,0.598)[/tex]

is the required confidence interval.

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