Final answer:
To create a confidence interval for a population proportion, calculate the point estimate (sample proportion), determine the margin of error, and calculate the confidence interval by subtracting and adding the error bound to the sample proportion.
Step-by-step explanation:
To create a confidence interval for a population proportion, the first step is to calculate the point estimate, which is the sample proportion. In this case, the point estimate is the number of SUVs sold divided by the total number of vehicles sold. The sample proportion is 142/432 = 0.3296.
Next, determine the margin of error by using the formula:
Error Bound = Z * sqrt((p * (1-p))/n)
where Z is the z-score corresponding to the desired confidence level, p is the sample proportion, and n is the sample size. In this case, since the confidence level is 90%, the Z-score is 1.645 (derived from a standard normal distribution table).
Finally, the confidence interval can be calculated by subtracting the error bound from the sample proportion and adding the error bound to the sample proportion:
Confidence Interval = (Sample Proportion - Error Bound, Sample Proportion + Error Bound)
Substituting in the values:
Confidence Interval = (0.3296 - 1.645 * sqrt((0.3296 * (1-0.3296))/432), 0.3296 + 1.645 * sqrt((0.3296 * (1-0.3296))/432))
Simplifying the calculation:
Confidence Interval = (0.3296 - 0.0282, 0.3296 + 0.0282)
Confidence Interval = (0.3014, 0.3578)
Therefore, the 90% confidence interval for the population proportion of adults in the US who own SUVs is 0.3014 to 0.3578.