Question

EACH STUDENT IN YOUR CLASS SHOULD HAVE GOTTEN A SLIGHTLY DIFFERENT CONFIDENCE INTERVAL. WHAT PROPORTION OF THOSE INTERVALS WOULD YOU EXPECT TO CAPTURE THE TRUE POPULATION MEAN? WHY? IF YOU ARE WORKING IN THIS LAB IN A CLASSROOM, COLLECT DATA ON THE INTERVALS CREATED BY OTHER STUDENTS IN THE CLASS AND CALCULATE THE PROPORTION OF INTERVALS THAT CAPTURE THE TRUE POPULATION MEAN.

Answer 1

The proportion of intervals expected to capture the true population mean is same as confidence level. Because for say, a 95% confidence interval the probability that the interval will contain the true population mean is 0.95 i.e. confidence intervals based on 95% of the samples of sufficiently large size will contain the true population proportion.

Suppose the students of the class are conducting a project on determining the average height of men in a city with a male population of around 50,000.

Now, doing census in this case is not possible as it will be time consuming as well as tedious.

So, each of them randomly selected 100 men and conduct a survey only for those 100 men.

Suppose the average height of those 100 men is 175 cm and the standard deviation is 25 cm in one sample.

Here, the population parameter is the mean height of men.

So, the 95% confidence interval of the population mean height is:

[,  ], where,  = 175, s = 25, n = 100

= [175 - 4.96, 175 + 4.96] = [170.04, 179.96]

Now, the remaining students also constructed similar intervals. We expect 95% of those intervals will contain the true population mean height.