Solution: A sample is a part of a population and a population is the source of a sample and contains all the members with common or similar characteristics. Example: students enrolled in an accounting class is a sample. 

Question 2 - True or False: The value of a statistics such as the mean or average remains unchanged with repeated sampling.

Solution: False: Each time you sample you get a different set of values on which the statistics is calculated, so the outcome may not be always the same.

Question 3 - If studies* showed that US homes contain the following demographics, is this descriptive or inferential statistics? 
 

Classification	Color TV Sets	2 or more TV sets	Cable	B&W TV set	! Tv Set
Percentage of Homes	85%	73%	67.2%	1%	27%

*Taken from textbook exercises

Solution: Descriptive since it is a summary of data collection, percent shown are called statistics

Question 4 - A study of 200 freshman students enrolled at a particular college suggests that 15% will drop out within the next two years; is this descriptive or inferential statistics?

Solution: Inferential statistics since the study is implying something about the statistics or data summary from the study. The 15% is an inferred statistics or a prediction about what may happen.

Question 5 - From a random sample of families in a small town the following results were obtained and answers to questions about this study are shown below:
 

Number in Household Members* Not Working	Number of families in Town	Number of families in sample
0	50	8
1	300	14
2	800	20
3	100	8
4	110	12
>4	25	5
Totals	1,385	67

* members over 15 years old

(a) State the population size: The population is the total number of families in the town and is 1,385

(b) State the sample size: The sample is the number of families studied or sampled and is 67.

Often the sample size is denoted with the symbol, n.

(c) What is the statistics and parameters for the number of families and proportion with less than 3 members not working? 

The statistics relates to the sample, so the numbers of families in the sample not working with <3 members in household is 8 + 14 + 20 = 42 and the proportion is 42 divide by 67 = 0.62.

The parameter relates to the population, so the numbers of families in the population not working with <3 members in household is 50 + 300 + 800 = 1,150 and the proportion is 1150 divide by 1385 = 0.83.

Question 6 - The number of patients treated at a local emergency room of a hospital last week is summarized below. Answers to questions on this descriptive statistics are given below:
 

Patient's Sex	Treatment Types			Total
	Minor Surgery (MS)	Internal Medicine (IM)	Referrals to Other Departments (R)
Male	45	50	25	120
Female	32	43	83	158
Totals	77	93	108	278

The hospital administrator is interested in sampling only 20 patient files for future planning purposes:

(a) Obtain a random samples of 20 patient files: If the patients files in each cells of the table above labeled for random sample as:
 

Male - MS (1 to 45)	Male - IM (46 to 95)	Male - R (96 to 120)
Female - MS (121 to 152)	Female - IM (153 to 195)	Female - R (196 to 278)

From a random table or random number generator  (Excel Program) of numbers 1 to 278 (the total size of patient files so designated the population of patients treated) select 20 numbers or labels.

Here is some random table of values:

Summary of selection: e.g. First 3 number of table is 28, 10, 277: 28 would make 1 for Male - MS, 10 2 for Male - MS and 277 makes 1 for Female - R and so on until 20 is assigned.

50 patients selected at random from 278 possible numbers
 

Patient Sex	Treatment Types			Total
	Minor Surgery (MS)	Internal Medicine (IM)	Referrals to Other Departments (R)
Male	7	1	3	11
Female	3	1	5	9
Totals	10	2	8	20

Random Numbers are:
 

Male - MS (1 to 45) 28, 10, 38, 37, 40, 42, 8	Male - IM (46 to 95) 76	Male - R (96 to 120) 104, 111, 112
Female - MS (121 to 152) 131, 150, 128	Female - IM (153 to 195) 193	Female - R (196 to 278) 277, 266, 242, 216, 224

(b) Obtain a stratified proportional sample for each of the six categories of strata above, e.g. Male - IM

Proportion in each strata:
 

Male - MS (45/278 = 0.16)	Male - IM (50/278 = 0.18)	Male - R (25/278=0.09)
Female - MS (32/278=0.12)	Female - IM (43/278=0.15)	Female - R (83/278=0.30)

So stratified proportional sample would be 20 times each proportion:
 

Patient Sex	Treatment Types			Total
	Minor Surgery (MS)	Internal Medicine (IM)	Referrals to Other Departments (R)
Male	3	4	2	9
Female	2	3	6	11
Totals	5	7	8	20

Note: number round up to account for sample size of 20, e.g.. Male - IM from 3.6 to 4.

To select 20 samples randomly for this study you would label as follows:
 

Male - MS (1 to 3)	Male - IM (4 to 7)	Male - R (8 to 9)
Female - MS (10 to 11)	Female - IM (12 to 14)	Female - R (15 to 20)

Question 7 - For its leadership program, a graduate study group reads on average these numbers of books each month: 
 

Graduate Student Name	Number of Books read each Month
Jill	3.4
Jane	6.5
Mike	2.5
Juan	4.2

(a) Is this study a cross-sectional or longitudinal study?

Solution: A cross-sectional - since each student were compared to each other at the same time.

(b) How would you conduct a longitudinal study of this group of students?

Solution: One possible solution is to compare their reading habits one year from now.

Question 8 - 100 patients were given a wonder drug to help solve their sleeping disorder: In fact two types of drugs were given to patients packaged in the same identical container with a code designating which bottles contained the true wonder drug. The bottles which contained the wonder drug and the placebo (no effect on improving sleeping disorder) is only know to the researchers and not the patients or those distributing the drug. What kind or experiment is this?

Solution - A double blind controlled experiment (if the drug was distributed to patients randomly it would be a double-blind random controlled experiment)

Question 9 - A teacher did an experiment and concluded that the more regular hours of sleep students get each night is reflected in their ability to perform better in class workshops.

Can you think of some confounding factors that might influence students performance in class workshops?

Many possible solutions: Example, Mastery of workshop fundamentals

Question 10 - Give an example of an experiment which contains, treatment, treatment group and control group and is a controlled random experiment.

One possible solution: An exam that compares students taking online statistics course (treatment group) with regular classroom instructed statistics students (control group) in which students selected to participate in the online statistics course were selected randomly (random selection) from a larger set of students willing to learn statistics.

The treatment is the types of learning experience for statistical course (online or classroom).