Question

Favorite Skittles Flavor?

A poll sampled 99 people, asking them their favorite skittle flavor by color (green, orange, purple, red, or yellow). A separate poll sampled 118 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	28	14	21	19	17
Flavor	19	22	26	37	14

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
Flavor

(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 method of choice affects which is chosen?

Answer 1

Solution-:

Hypothesis:

The way people choose their favorite Skittles type, by color or flavor, appear to be independent.

Vs

The way people choose their favorite Skittles type, by color or flavor, appear to be related

The given frequencies table are observed frequencies

	Green (Lime)	Orange	Purple (Grape)	Red (Strawberry)	Yellow (Lemon	Total
Color	28	14	21	19	17	99
Flavor	19	22	26	37	14	118
Total	47	36	47	56	31	217

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

The corresponding expected frequencies are obtained using formula

for

Note: are not to be rounded-off to the integers.

The given frequencies table are expected frequencies

	Green (Lime)	Orange	Purple (Grape)	Red (Strawberry)	Yellow (Lemon
Color	21.44	16.42	21.44	25.55	14.14
Flavor	25.56	19.58	25.56	30.45	16.86

(b)  Yes,  the expected counts are  large enough for a chi-square test.

(c) The degrees of freedom do we have for this test is,

  Degrees of freedom

(d) For calculating test statistic we prepare table for

36.56	11.93	20.57	14.13	20.43
14.12	24.72	26.45	44.96	11.63

Uder he chi-square test statistic is,

(e) P-value:-     

By using MS-Excel Command "=CHIDIST(8.51,4)"

Accept

Conclusion-: We conclude that The way people choose their favorite Skittles type, by color or flavor, appear to be independent (Not related).