Author Question: The residents of one town are classified by a social scientist as follows. Lower income: 4320 ... (Read 107 times)

ts19998 · **on:** Jul 25, 2018

The residents of one town are classified by a social scientist as follows.

Lower income: 4320
Middle income: 1520
Upper income: 2160

The scientist wishes to pick a sample of 200 of the residents for a study. Describe a method for selecting the sample which involves stratified sampling with proportional allocation.

Question 2

The owner of a farmer's market was interested in determining how many oranges a person buys when they buy oranges.

He asked the cashiers over a weekend to count how many oranges a person bought when they bought oranges and record this number for analysis at a later time. The data is given below in the table. The random variable x represents the number of oranges purchased and P(x) represents the probability that a customer will buy x oranges. Determine the variance of the number of oranges purchased by a customer.

x 1 2 3 4 5 6 7 8 9 10
P(x) 0.05 0.19 0.20 0.25 0.12 0.10 0 0.08 0 0.01

A) 3.97 B) 1.95 C) 0.56 D) 3.57

ashely1112 · **Reply #1 on:** Jul 25, 2018

Answer to Question 1

Answers will vary. Possible answer: Proportional allocation dictates that the number of lower income, middle income, and upper income residents selected by the scientist be 108, 38, and 54, respectively. Thus the scientist can obtain a stratified sample of 200 residents as follows: Number the lower income residents from 1 through 4320 and use table of random numbers to randomly select 108 of the 4320 lower income residents; number the middle income residents from 1 to 1520 and use a table of random numbers to randomly select 38 of the 1520 middle income residents; number the upper income residents from 1 to 2160 and use a table of random numbers to randomly select 54 of the 2160 upper income residents.

Answer to Question 2

D