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

The answer is:

OPTION C

Calculations:

The following null and alternative hypotheses need to be tested:

H0​: The two variables are independent

Ha​: The two variables are dependent

Test Statistics

The Chi-Squared statistic is computed as follows:

The corresponding p-value for the test is

The decision about the null hypothesis

Since it is observed that χ2=9.224>χc2​=7.815, it is then concluded that the null hypothesis is rejected.

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