Using the following data, find the upper bound of confidence interval. Your answer must be in 3 decimal places.
n=400, p̂ = 0.75, 90% confidence
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Using the following data, find the upper bound of confidence interval. Your answer must be in 3 decimal places.
n=400, p̂ = 0.75, 90% confidence
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Step-by-step explanation:
Confidence Interval Upper Bound
n=400, p̂ = 0.75, 90% confidence
Upper bound = p̂ + zα/2 * √(p̂(1-p̂)/n)
where:
p̂ = 0.75 (sample proportion)
n = 400 (sample size)
zα/2 = z-score corresponding to the desired confidence level (90% in this case)
To find the z-score, we can use a standard normal distribution table or a calculator. For a 90% confidence level, the z-score is approximately 1.645.
Substituting the values into the formula, we get:
Upper bound = 0.75 + 1.645 * √(0.75(1-0.75)/400)
Upper bound = 0.75 + 1.645 * 0.032
Upper bound = 0.75 + 0.053
Upper bound = 0.803
Therefore, the upper bound of the 90% confidence interval is 0.803