Question

1. Marine biologists have noticed that the color of the outermost growth band on a clam tends to be related to the time of the year in which the clam dies. A biologist conducted a small investigation of whether this is true for the species Protothaca staminea. She collected a sample of 78 clam shells from the species and classified them according to the month when the clam died and the color of the outermost growth band. The data are provided below:

Color

Clear Dark Unreadable

February 9 25 7

March 15 18 4

Is there a significant difference in the color distribution between clams that died in February and March? Show your work and include all steps for full credit. Make sure all assumptions are met. (4pts)

2. The Wisconsin Fast Plant (Brassica campestris) has a very rapid growth cycle that makes it particularly well-suited for studying factors that affect plant growth. A random sample of plants was treated with the substance Ancymidol and compared a control group of plants that was given ordinary water. The heights of all of the plants were measured (in cm) after two weeks of growth:

Ancymidol 7.7, 12.8, 5.5, 19.0, 13.1, 8.2, 14.3

Control 19.2, 14.3, 21.2, 9.2, 20.4, 19.7

Conduct the appropriate test to determine if there is a difference in plant height after two weeks of growth if plants were given Ancymidol compared to water. Include all steps for full credit. (4pts)

Answer 1

1;

Here we need to chi square test.

Hypotheses are:

H0: There is no difference in the color distribution between clams that died in February and March.

Ha: There is a difference in the color distribution between clams that died in February and March

Following table shows the row total and column total:

	Clear	Dark	Unreadable	Total
February	9	25	7	41
March	15	18	4	37
Total	24	43	11	78

Expected frequencies will be calculated as follows:

Following table shows the expected frequencies:

	Clear	Dark	Unreadable	Total
February	12.615	22.603	5.782	41
March	11.385	20.397	5.218	37
Total	24	43	11	78

Following table shows the calculations for chi square test statistics:

O	E	(O-E)^2/E
9	12.615	1.0359275
15	11.385	1.1478458
25	22.603	0.2541967
18	20.397	0.2816889
7	5.782	0.2565763
4	5.218	0.2843089
Total		3.2605442

Following is the test statistics:

Degree of freedom: df =( number of rows -1)*(number of columns-1) = (2-1)*(3-1)=2

The p-value is: 0.1958

Conclusion: Since p-value is not less than 0.05 so we fail to reject the null hypothesis. There is a significant difference in the color distribution between clams that died in February and March.

Excel function used for p-value: "=CHIDIST(3.261,2)"