Suppose that a manager is interested in estimating the average amount of money customers spend in her store. After sampling 36 transactions at random, she found that the average amount spent was $ 35.25 . She then computed a 95 % confidence interval to be between $ 31.84 and $ 38.66 .
1. Which statement gives a valid interpretation of the interval?
O The store manager is 95 % confident that the average amount spent by the 36 sampled customers is between $ 31.84 and $ 38.66 .
O There is a 95 % chance that the mean amount spent by all customers is between $ 31.84 and $ 38.66 .
O The store manager is 95 % confident that the average amount spent by all customers is between $ 31.84 and $ 38.66 .
O There is a 95 % chance that a randomly selected customer will spend between $ 31.84 and $ 38.66 .

The store manager is 95% confident that the average amount spent by all customers is between $ 31.84 and $ 38.66.

Explanation:

In statistics, a confidence interval is the probability that the parameter of a population lies between two set of values when a random sample of the population is drawn for a specific percentage of times. This means that the confidence interval is formed about the whole population not the sample from which it is calculated.

The probabilities of a confidence interval can take any number, but 95% and 99% confidence level that are usually used.

It should be noted that, for example, 95% confidence level implies that there is a 95% chance that the true mean of the population lies within the calculated confidence interval.

Therefore, the statement which gives a valid interpretation of the interval in the question is the first one which states that "the store manager is 95% confident that the average amount spent by all customers is between $ 31.84 and $ 38.66."

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