Question

a trade magazine routinely checks the drive through service times of fast food restaurants. a 95% confidence interval that results from examining 605 customers in one fast food chains drive through has a lower bound of 170.1 seconds and upper bound of 173.1 seconds. what does this mean?

Answer 1

Confidence interval is a range of values that contain an unknown population parameter. Confidence interval contains the true value of the parameter when a random sample is drawn many times.

For the large samples the population parameter with more precision can be obtained. Therefore, confidence interval is based on sample observations.

Let denote the mean service time then it represents the population parameter

Let us understand the concept on the basis of confidence interval of mean for known standard deviation.

Then the confidence interval for level of significance is given by

The level of significance is generally expressed in percentage form then 100(1- )% represents the confidence interval.

=5% we have 95% confidence interval.

In many cases population parameter is unknown so to have an idea about the population parameter confidence interval is generally used in which there is high chances of population parameter to fall in that region.

Let us understand the concept using the sample. Let us assume that 100 samples of fast food restaurant is taken then 95% confidence interval indicates that out of 100 samples , the mean service times of fast food restaurant lies in an interval (170.1, 173.1) in 95 of those 100 samples. Also, if the same population is sampled in many number of time and in many occasions and if the confidence interval is obtained in each case, then in 95% of the samples the population parameter falls in the confidence interval in 95% of the samples. i.e. for 605 customer the mean service time of restaurant lies in (170.1, 173.1).