Question

Danielle and William are visiting an ice cream shop where they will randomly choose one of the following five regular and premium flavors.

Flavors Price

Vanilla Bean $2.00

Chocolate Mint $3.00

Pralines and Cream $4.00

Strawberry Shortcake $5.00

Fudge Brownie Caramel Cheesecake Deluxe $6.00

Define the population as the five services and a sample of size two as the flavor that Danielle chooses and the service that William chooses.

a. Identify the frequency distribution for the population

b. Identify the frequency distribution for all combinations of samples means for Danielle and William choosing a flavor

c. Verify that the population mean and man of all possible sample means are equal

d. Calculate the standard error.

Answer 1

a) Frequency distribution for the population

servings	price	relative frequency
vanilla bean (VB)	2	0.2
chocolate mint (CM)	3	0.2
pralines and cream (PC)	4	0.2
strawberry shortcake (SS)	5	0.2
fudge brownie ….(FB)	6	0.2

To find population mean and standard deviation

x	P(x)	x.P(x)	x^2.P(x)
2	0.2	0.4	0.8
3	0.2	0.6	1.8
4	0.2	0.8	3.2
5	0.2	1	5
6	0.2	1.2	7.2
		4	18

Population mean = =  4

Standard deviation = =

Note : As the five are equally likely , we assigned equal probability to them , 1/5 =0.2

b) There are 5*5 =25 possible combinations of servings that two chose to eat

sample size =25

The frequency distribution of sample means

samples	sample mean	probability
2,2	2	0.04
2,3;3,2	2.5	0.08
2,4; 4,2; 3,3	3	0.12
2,5; 5,2; 3,4; 4,3	3.5	0.16
4,4; 2,6; 6,2; 3,5; 5,3	4	0.2
4,5; 5,4; 3,6; 6,3	4.5	0.16
5,5;4,6;6,4	5	0.12
5,6; 6,5	5.5	0.08
6,6	6	0.04

c) Population mean =4

Mean of sample mean = 2*0.04 + ....+ 6* 0.04 = 4

d) standard error= population standard deviation/ 1.4142 /