Question

A trade magazine routinely checks the drive-through service times of fast-food restaurants. an 80% confidence interval that results from examining 552 customers in one fast-food chain's drive-through has a lower bound of 172.3 seconds and an upper bound of 175.5 seconds. what does this mean?

Answer 1

An 80% confidence interval of 172.3 to 175.5 seconds for drive-through service times means that the true average time likely falls within this range. Confidence intervals allow us to estimate population parameters like mean delivery times with a certain level of confidence, based on sample data.

Step-by-step explanation:

The provided confidence interval tells us that with 80% confidence, the true average drive-through service time falls between 172.3 seconds and 175.5 seconds. In other words, if we were to take many samples of 552 customers from this fast-food chain and compute a confidence interval for each sample, about 80% of these intervals would capture the true average service time.

Now let's apply this concept to the questions about pizza delivery times:

• If we change the sample size to 50 restaurants while maintaining the same sample mean of 36 minutes, the 90 percent confidence interval for the population mean delivery time would be recalculated using the larger sample size and would be narrower than that for a smaller sample size, given the same level of confidence and population standard deviation of 6 minutes.
• For a sample of 28 pizza delivery restaurants with a sample mean delivery time of 36 minutes, the 90 percent confidence interval would provide a range in which the true population mean delivery time is likely to fall, assuming a normally distributed population with a standard deviation of 6 minutes.

To conclude, confidence intervals give us a range of values within which we can be reasonably sure the true population parameter (in this case, mean delivery time) lies, based on our sample statistic and a certain level of confidence.

Answer 2

80% sure that the true mean waiting time for all customers in one fast-food chain's drive through is between 172.3 seconds and 175.5 seconds.

Step-by-step explanation:

A x% confidence interval of a sample being (a,b) means that we are x% sure that the true mean of the population is between a and b.

In this problem, we have that:

80% confidence interval that results from examining 552 customers in one fast-food chain's drive-through has a lower bound of 172.3 seconds and an upper bound of 175.5

This means that we are 80% sure that the true mean waiting time for all customers in one fast-food chain's drive through is between 172.3 seconds and 175.5 seconds.