Question

7.2 Question 1 Give the degrees of freedom for the chi-square test based on the two-way table.

	D	E	F	G	Total
A	39	34	43	34	150
B	78	89	70	93	330
C	23	37	27	33	120
Total	140	160	140	160	600

Degrees of freedom =

b. Find the expected count and the contribution to the chi-square statistic for the (Group 2, Yes) cell in the two-way table below.

	Yes	No
Group 1	733	255
Group 2	1178	316

Round your answer for the excepted count to one decimal place, and your answer for the contribution to the chi-square statistic to three decimal places.

Expected count = Enter your answer; Expected count

contribution to the chi-square statistic = Enter your answer; contribution to the chi-square statistic

Favorite Skittles Flavor?

C. A poll sampled 81 people, asking them their favorite skittle flavor by color (green, orange, purple, red, or yellow). A separate poll sampled 103 people, again asking them their favorite skittle flavor, but rather than by color they asked by the actual flavor (lime, orange, grape, strawberry, and lemon, respectively). The table below shows the results from both polls. Does the way people choose their favorite Skittles type, by color or flavor, appear to be related to which type is chosen?

	Green (Lime)	Orange	Purple (Grape)	Red (Strawberry)	Yellow (Lemon)
Color	22	11	18	16	14
Flavor	16	19	23	34	11

Table 1 Skittles popularity


(a) Give a table with the expected counts for each of the 10 cells.

Round your answers to two decimal places.

	Green (Lime)	Orange	Purple (Grape)	Red (Strawberry)	Yellow (Lemon)
Color	Enter your answer in accordance to item (a) of the question statement	Enter your answer in accordance to item (a) of the question statement	Enter your answer in accordance to item (a) of the question statement	Enter your answer in accordance to item (a) of the question statement	Enter your answer in accordance to item (a) of the question statement
Flavor	Enter your answer in accordance to item (a) of the question statement	Enter your answer in accordance to item (a) of the question statement	Enter your answer in accordance to item (a) of the question statement	Enter your answer in accordance to item (a) of the question statement	Enter your answer in accordance to item (a) of the question statement

(b) Are the expected counts large enough for a chi-square test?

Choose the answer from the menu in accordance to item (b) of the question statement                                                          YesNo

(c) How many degrees of freedom do we have for this test?

Degrees of freedom = Enter your answer in accordance to item (c) of the question statement

(d) Calculate the chi-square test statistic.

Round your answer to two decimal places.

chi-square statistic = Enter your answer in accordance to item (d) of the question statement

(e) Determine the p-value.

Round your answer to four decimal places.

p-value = Enter your answer in accordance to item (e) of the question statement


Using a 5 % level, do we find evidence that the method of choice affects which is chosen?

Choose the answer from the menu in accordance to item (e) of the question statement

d. Homes for Sale: Chi-Square Test

In previous questions, we examined various relationships between the variables regarding houses for sale in the dataset HomesForSale. One topic of repeated interest was the differences between states. We previously only had the capability to test for a difference between two states at a time, but we can now test for relationships across all four states at once.

The table below shows the number of big (greater than the national average of 2700 sqft) and not big houses for sale for each of the four states. Is location associated with the proportion of big houses? Are the conditions met for a chi-square test? Perform the test to see if the proportion of big houses is related to location (states).

	California	New Jersey	New York	Pennsylvania	Total
Big	7	6	7	3	23
Not	23	24	23	27	97
Total	30	30	30	30	120

Table 1 Houses for sale in four states


Click here for the dataset associated with this question.

Are the conditions met for a chi-square test?

Choose the answer from the menu; Are the conditions met for a chi-square test?                                                          YesNo

Round your answer for the chi-square statistic to one decimal place, and your answer for the p-value to three decimal places.

chi-square statistic = Enter your answer; chi-square statistic

p-value = Enter your answer; p-value


Conclusion: Choose the answer from the menu; Conclusion                                                          RejectDo not reject H 0 .

Does the test indicate an association between these two variables?

Choose the answer from the menu; Does the test indicate an association between these two variables?                                                          YesNo

  

  

Answer 1

Number of Rows =   3
Number of Columns =   4
Degrees of Freedom=(#row - 1)(#column -1) = (3- 1 ) * ( 4- 1 ) =   6
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B) group 2, yes

Expected frequency of a cell = sum of row*sum of column / total sum = 1911*1494/2482=1150.3

contribution to chi square= (fo-fe)^2/fe = (1178-1150.3)²/1150.3 = 0.667

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c)

a)

	Expected frequency of a cell = sum of row*sum of column / total sum
	Expected Frequencies
	green	orange	purple	red	yellow
color	38*81/184=16.728	30*81/184=13.207	41*81/184=18.049	50*81/184=22.011	25*81/184=11.005
flavor	38*103/184=21.272	30*103/184=16.793	41*103/184=22.951	50*103/184=27.989	25*103/184=13.995

b) YES, expected count ≥5

c) Chi-Square Test Statistic,χ² = Σ(fo-fe)^2/fe =   8.01

d)   
Level of Significance =   0.05
Number of Rows =   2
Number of Columns =   5
Degrees of Freedom=(#row - 1)(#column -1) = (2- 1 ) * ( 5- 1 ) =   4
  
p-Value =   0.0910

e)
Decision:    p value > α , do not reject Ho