To calculate the 99% confidence interval for the population proportion of new car buyers who prefer foreign cars over domestic cars, we can use the formula:
CI = p̂ ± Z*(√(p̂*(1-p̂)/n)
Where:
p̂ = sample proportion = 354/1418 = 0.25
n = sample size = 1418
Z = z-score for a 99% confidence level, which is approximately 2.576
Plugging in the values, we get:
CI = 0.25 ± 2.576*(√(0.25*(1-0.25)/1418))
CI = 0.25 ± 0.018
Therefore, the 99% confidence interval for the population proportion of new car buyers who prefer foreign cars over domestic cars is approximately 0.232 to 0.268.
An automotive manufacturer wants to know the proportion of new car buyers who prefer foreign cars over domestic.
Step 2 of 2 : Suppose a sample of 1418
new car buyers is drawn. Of those sampled, 354
preferred foreign over domestic cars. Using the data, construct the 99%
confidence interval for the population proportion of new car buyers who prefer foreign cars over domestic cars. Round your answers to three decimal places.
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1 answer