Question

55) there are 216 people in attendance at the senior gala at Larson farber high. All seniors could invite anyone they wanted as long as they attend the school. In total 55% of attendees were seniors, 23% were juniors, 15% were sophomores and 7%were freshman. You will be surveying 30 students as they walk ou tthe door to find out about their evening. A) Describe in detail how you would SYSTEMATICALLY select people. b) If you took a STRATIFIED sample (by grade lvl) of 30 participants, how many of each should you sample?

Answer 1

a) The systematic sampling is to find an interval k based on the sample size and total number of attendees. sample size 30 is what we want. and in total there are 216 attendees. 216/30=7.2.

That means after selecting the first person for taking the survey you need to select every 7th person walking out the door for the sample to be 30

b) Stratification can be done in two ways.:

Equal allocation:Equal number of persons can be selected from each group. That means atleast 7 from each of the 4 groups

Proportional allocation: Sampling is done proportional to the group size.

According to the percentages given in the question 119,50,32 and 15 are the attendees, juniors,sophomores and freshman. If the same percentages of the sample size is taken you are done with proportional allocation

ie 55% of 30=16.5~17

23% of 30=6.9~7

15% of 30=4.5~4

7%of 30=2.1~2