The president of a bowling league wanted to estimate the average highest bowling score of all its 200 members. instead of surveying all 200 members, she randomly selected 20 members and recorded their highest scores. she found the sample mean to be 237. what inference can she make based on the sample mean?
In statistics, whenever full population cannot be surveyed, a random sample can be taken and from the observations population behaviour can be estimated.
Here given that there are 200 members. Instead of collecting data from all 200, 20 members are randomly taken.
The sample mean x bar can be estimated to give an idea the population mean also.
ACcording to central value theorem, means of different samples will follow a distribution with mean = population mean and std deviation = std dev of sample/square root of n
Hence we fix confidence interval as Mean + or - Z critical * std error
This gives us an idea about within which means will lie for different samples and hence give an idea about population mean also.
area = length x width
length = 2 x width
32 = 2 x width x width
32 = 2 x width^2
36 = width ^2
width = 6
length = 12
area is 32
perimeter = 2 x 12 + 2 x 6 = 24 + 12 = 36