The confidence interval at 90% is given by 0.662 p < 0.738.
A confidence interval can be defined as a range of estimated values that defines the probability that a population parameter would fall or lie within it.
The test statistic of a population can be calculated by using this formula:
[tex]t=\frac{x\;-\;u}{\frac{\delta}{\sqrt{n} } }[/tex]
Where:
For the sample proportion, we have:
Sample proportion, P = 280/400
Sample proportion, P = 0.7.
The standard error of the sample is given by:
Standard error = √(0.7 × (1 - 0.7)/400)
Standard error = √(0.7 × (0.3)/400)
Standard error = √(0.000525)
Standard error = 0.0229.
Alpha, α = 1 - 90/100
Alpha, α = 1 - 0.9
Alpha, α = 0.1
Critical probability (p*) = 1 - α/2
Critical probability (p*) = 1 - 0.1/2
Critical probability (p*) = 0.95.
For the z-score, we have:
Zα/2 = 1.645.
Margin of error is given by:
Margin of error, E = 1.645 × 0.0229
Margin of error, E = 0.038.
Therefore, the confidence interval at 90% is given by:
p - E < p < p + E
0.7 - 0.038 < p < 0.7 + 0.038
0.662 p < 0.738.
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