Question

In: Statistics and Probability

Shirt Cost Basic T-Shirt (B) $18 New Arrival T-Shirt (N) $20 Premium T-Shirt (P) $22 Exclusive...

Shirt	Cost
Basic T-Shirt (B)	$18
New Arrival T-Shirt (N)	$20
Premium T-Shirt (P)	$22
Exclusive Playoffs T-Shirt (E)	$24

Define the population as the four shirts and a sample of size two as the t-shirt that Josie chooses and the t-shirt that Will chooses.

Identify the frequency distribution for the population
Identify the frequency distribution for all combinations of sample means for Josie and Will choosing a shirt
Verify that the population mean and mean of all possible sample means are equal
Calculate the standard error of the mean
Show your work using only numbers for each part (a-d) of the problem. Show all charts/tables. You do not need to enter the formulas or Greek letters.

Expert Solution

Answer:

a) The frequency distribution for the population will be a uniform distribution. Here is what the table will look like:

Cost (in $)	Shirt	Probability
18	B	1/4
20	N	1/4
22	P	1/4
24	E	1/4

b) For the sample distribution, we have to consider each combination of shirts and take their average.

As Josie and Will both have 4 choices, there are 16 choices in all.

BB means that Josie and Will both choose Basic T-shirt. The average is $18.

BN means that Josie chose Basic T-shirt and Will both choose New Arrival T-shirt. The average is $19. Also, NB is a different combination with the same average of $19.

BP, NN, and PB all have the average of $20.

Using similar cases, we have:

Average Cost (in $)	Shirts	Probability
18	BB	1/16
19	BN, NB	2/16
20	BP, NN, PB	3/16
21	BE, NP. PN, EB	4/16
22	NE, PP, EN	3/16
23	PE, EP	2/16
24	EE	1/16

c) We write the population mean as sum of the product of the numbers and corresonding probability from the first table:

We write the sample mean as sum of the product of the numbers and corresonding probability from the second table:

So, the population mean of $21 is equal to the sample mean of $21. Hence, we have verified that the means are equal.

d) The population standard deviation is:

The sample standard deviation is:

The standard error of the mean is equal to the sample standard deviation = 1.6330.

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orchestra answered 1 year ago

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