Question

A random sample of adults in the US were asked whether they consider a car a necessity or a luxury,1 and we find that a confidence interval for the proportion saying that it is a necessity is to . Explain the meaning of this confidence interval in the appropriate context.

Answer 1

Answer:

There is 95% confidence that the true proportion of people who say that a car is a necessity lies in the interval (0.83, 0.89).

Step-by-step explanation:

A (1 - α)% confidence interval for population proportion is given by:

$CI=\hat p\pm z_{\alpha/2}\times \sqrt{\frac{\hat p(1-\hat p)}{n}$

The sample size is, n = 1483.

The 95% confidence interval for the population proportion of people who say that a car is a necessity is,

CI = (0.83, 0.89)

A (1 - α)% confidence interval for a population parameter implies that there is (1 - α) probability that the true parameter value is contained in the interval.

Or, there is (1 - α)% confidence that the confidence interval consists of the true population parameter value.

The 95% confidence interval for the population proportion of people who say that a car is a necessity implies that the true proportion of people who say that a car is a necessity lies in the interval (0.83, 0.89) with a probability of 0.95.

Or, there is 95% confidence that the true proportion of people who say that a car is a necessity lies in the interval (0.83, 0.89).