Question

b. Assume a superior tells you she thinks it may be too much trouble to look at 100 data points; so you apply the systematic random sampling method to find a sample of 10 observations from each of your two new tables, starting with the 5th observation (Vending 5 for Coke, Vending 55 for Pepsi) and taking every 5th observation after that. Compute the sample mean and sample standard deviation for Average Daily Sales for your new, smaller sample data sets for Coke and Pepsi (of 10 randomly selected observations each). Take note of differences. Does each sample of 10 properly represent the larger samples of 50 observations for each brand? Could you say, then, that the sample of 20 is a good representation of the true population?

Table C6-1: Average daily sales by vending machine number, brand and location type
Vending Machine	Location Type	Brand	Avg Daily Sales	Vending Machine	Location Type	Brand	Avg Daily Sales
1	A	COKE	1051	51	B	PEPSI	411
2	B	COKE	1385	52	A	PEPSI	687
3	A	COKE	890	53	B	PEPSI	1174
4	B	COKE	1113	54	A	PEPSI	605
5	A	COKE	857	55	A	PEPSI	487
6	A	COKE	994	56	B	PEPSI	824
7	B	COKE	1521	57	B	PEPSI	455
8	B	COKE	1106	58	A	PEPSI	477
9	A	COKE	900	59	B	PEPSI	698
10	A	COKE	455	60	A	PEPSI	902
11	B	COKE	1299	61	B	PEPSI	196
12	A	COKE	925	62	A	PEPSI	508
13	B	COKE	909	63	A	PEPSI	661
14	B	COKE	821	64	A	PEPSI	781
15	A	COKE	785	65	B	PEPSI	1197
16	A	COKE	945	66	B	PEPSI	565
17	A	COKE	850	67	B	PEPSI	995
18	B	COKE	785	68	A	PEPSI	488
19	B	COKE	626	69	B	PEPSI	500
20	B	COKE	892	70	B	PEPSI	695

Answer 1

Suppose you have 100 data points and you want to sample 10 observations via systematic random sampling method, you can follow the steps below:

1. Number each of the observation from 1 to 100

2. Compute the interval k: k = 100/10 = 10

3. Randomly select a number from 1 to k. Say you select 7

4. The first data point selected is the 7th observation.

5. The remaining data points selected are every 10th observation from the first.

Your sample is: (7, 17, 27... 97) - A total of 10 data points