Question

The data presented in the table below resulted from an experiment in which seeds of 4 different types were planted and the number of seeds that germinated within 4 weeks after planting was recorded for each seed type.

At the .05 level of significance, is the proportion of seeds that germinate dependent on the seed type?

Seed Type		Observed Frequencies
		Germinated	Failed to Germinate
	1	39	9
	2	54	34
	3	88	63
	4	57	42

• A.

  No, the proportion of seeds that germinate are not dependent on the seed type because the p-value = 0.0132.

• B.

  No, the proportion of seeds that germinate are not dependent on the seed type because the p-value = 0.0265.

• C.

  Yes, the proportion of seeds that germinate dependent on the seed type because the p-value = 0.0265.

• D.

  Yes, the proportion of seeds that germinate dependent on the seed type because the p-value = 0.0132.

Answer 1

Null hypothesis : Ho : Proportion of seeds that germinate are not dependent on the seed type

Alternative Hypothesis : Ha: Proportion of seeds that germinate are dependent on the seed type

- Test for association

Test Statistic

O : Observed Frequency

E: Expected Frequency

Given,

Observed Frequencies : O

Seed type	Germinated	Failed to Germinate	Row Total
1	39	9	48
2	54	34	88
3	88	63	151
4	57	42	99
Column Total	238	148	Grand Total =386

E: Expected Count/Frequency: E

Seed Type	Germinated	Failed to Germinate
1	(48*238) / 386	(48*148) / 386
2	(88*238) / 386	(88*148) / 386
3	(151*238) / 386	(151*148) / 386
4	(99*238) / 386	(99*148) / 386

E :

Seed Type	Germinated	Failed to Germinate
1	29.5959	18.4041
2	54.2591	33.7409
3	93.1036	57.8964
4	61.0415	37.9585

O	E	O-E	(O-E)2	(O-E)2/E
39	29.5959	9.4041	88.4379	2.9882
9	18.4041	-9.4041	88.4379	4.8053
54	54.2591	-0.2591	0.0671	0.0012
34	33.7409	0.2591	0.0671	0.0020
88	93.1036	-5.1036	26.0470	0.2798
63	57.8964	5.1036	26.0470	0.4499
57	61.0415	-4.0415	16.3333	0.2676
42	37.9585	4.0415	16.3333	0.4303
			Total	9.2243

Degrees of freedom = (Number of rows -1)(Number of columns - 1) = (4-1)x(2-1) =3

For 3 degrees of freedom,

p-value = 0.0265

Given, level of significance: = 0.05

As p-value : 0.0265 < level of significance: : 0.05 ; Reject the null hypothesis;

There is sufficient evidence to conclude that Proportion of seeds that germinate are dependent on the seed type.

is the proportion of seeds that germinate dependent on the seed type?

Answer :

Yes, the proportion of seeds that germinate dependent on the seed type because the p-value = 0.0265.