Question

In: Statistics and Probability

It is often difficult to find the exact mean average of a large population of data....

It is often difficult to find the exact mean average of a large population of data. We use confidence Intervals to estimate where we think the true mean lies. Discuss the advantages of using a confidence interval. Give an example of a large population of data that is suited to a confidence interval estimate- in other words, it would be very hard to find the exact true mean of the data.

Expert Solution

Confidence Interval :

A confidence Interval is the range of values that you believe to contain the population parameter of interest and is defiened by an upper and lower bound around a sample statistic.

i.e. A confidence interval is a statement giving a range of values within which the researcher is confident that a population parameter lies.

A confidence interval includes an interval in the form of either a range of numbers (10 - 20) or a number plus/minus another number (15 ± 5) and a percentage number indicating the degree of confidence that the population parameter is in the interval. For example you could say that the 95% confidence interval for a mean is 10-20. ( we can use different confidence levels as 0.95, 0.99)

Advantages :

1) A 95% confidence interval represent a range of values within which you are 95% certain that the true population mean exist.

2) A confidence interval is commonly used to assess the variabality of sample mean.

3) Confidence intervals should always be used in order to describe the major findings of a research study.

4) We can say before the confidence interval is computed that there will be a 95% probability that the interval to be formed will include the population parameter. In other words, for every 100 intervals we form, 95 of them will include the population parameter.

example :

The equatorial radius of the planet Jupiter is measured 40 times independently by a process that is practically free of bias. These measurements average = 71492 kilometers with a standard deviation of s = 28 kilometers. Find a 90% confidence interval for the equatorial radius of Jupiter.

(Note :-

Confidence Intervals for a population mean (n > 30):

For large random samples a confidence interval for a population mean is given by

where z* is a multiplier number that comes form the normal curve and determines the level of confidence

orchestra answered 2 years ago

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