Question 1.
a)the relevant population for this study
Currently-enrolled Students at a particular university are the relevant population. Collection of values of “SCORES provided by the students” will be the data. Population size=N.
b)From a list of all currently-registered students at the university, a sample of students is selectedrandomly.
i.Type of sample being conducted: SRSWOR- Simple Random Sampling Without replacementBecause a sample of size n selected from population of size N randomly without consideringprogram area.
ii.Sample Biased/Non-Biased: Sample may be Non-biased (SRS). (Note: In Sample consecutive random numbers may be generated which means one or more students in the same program may be included.)
c)Based on current enrollment levels in each program area at the university, a random sample is selected such that each program area is proportionally represented in the sample.
i.) Type of sample being conducted: Stratified Random Sampling under proportional allocation.“Each program” will form a stratum. Let k= number of strata. Ni is number of sampling units (current number of Students enrolled in particular program) in the ith stratum (ith program). ni=number of sampling units to be drawn from ith stratum by SRSWOR. n=size of the stratified sample. Proportional allocation- because each program area should be represented in the sample.
ii.Sample Biased/Non-Biased: Stratified sample is highly representative of the population.Overlapping can be an issue if there are subjects-students that fall into multiple subgroups(programs).
d)From a similar list as in (b), every 100th currently-registered student at the university is selected, starting at a randomly-selected position in the list between 1 and 100.
i.Type of sample being conducted: Systematic Sampling because “i (< = k)”=random start= a randomnumber selected by SRS (Simple Random Sampling) from 1 to k i.e.1 to 100. Unit corresponding tothis number is selected and subsequently every kth unit is selected. Systematic sample of size n willconsist of the units i, i+k, i+2k,….,i+(n-1)k i.e. i,i+100,i+200,……,.i+100(n-1).
ii.Sample Biased/Non-Biased: If we can assume that the population list is randomly shuffled, thensystematic sampling is equivalent to simple random sample, where there is no bias.
e)An email survey is sent to every currently-registered student at the university, and a sample isobtained from the first 100 students who submit a completed online response form.
i.Type of sample being conducted: Random sampling & Convenience Sampling (convenient- asample obtained from first 100 students who submit form).
ii.Sample Biased/Non-Biased: Biased as it may happen that all the students of particular programmay fill the form. Underrepresentation OR Overrepresentation may occur.
f)A similar list as in (b) is divided, based on alphabetical order, into 40 equal sized groups. Then, 5 ofthese groups are randomly selected, and every student in each selected group is included in thesample.
i.Type of sample being conducted: Cluster sampling. Here, 40 clusters (equal sized groups) arepresent. 5 clusters are to be selected. Every student in each selected group is included in the sample.
ii.Sample Biased/Non-Biased: may or may not be Biased. (Population of size N is divided into 40clusters of size N/40. It may happen consecutive clusters are selected. List of alphabetical order maycontain students with same alphabet same program-same livelihood goals.)

Question . 2 Brief explanation for each choice.
a)Low temperature on the day of the winter solstice at a certain location, in °C, over 20 consecutive years.
i)Quantitative or Qualitative: Since temperature can be measured so it is quantitative variable.
ii)Discrete or Continuous: Since it can take any value so it is a continuous variable.
iii)Nominal, Ordinal, Interval, or Ratio: Since zero does not mean absence of temperature so it is interval level variable.
b)Number of years, out of the last 20 years, when the low temperature on the day of the winter solstice was below 0 °C, at 50 different locations.
i)Quantitative or Qualitative: Since numbers of years can be measured so it is quantitative variable.
ii)Discrete or Continuous: Since number of years are countable so rt is a discrete variable.
iii)Nominal, Ordinal, Interval, or Ratio: Since zero means absence of number of years have low temperature below 0 degree so it is ratio level variable.
c)Rankings from 1-50, of coldest locations, based upon the number of years out of the last 20 years when the low temperature on the day of the winter solstice was below 0 °C, with 1 = location with most such days and 50 = location with fewest such days

METHODS AND APPLICATIONS 2.16 Consider the following data: DS Hi...