Chapter 27, Problem 27.43E

To determine

To explain do the data show that dead cicadas increase seed mass.

Answer to Problem 27.43E

The data do not show that dead cicadas increase seed mass.

Explanation of Solution

In the question, it is given the data for the seed masses produced by cicada-fertilized plants and undistributed control plants. Thus, to find if the data show that dead cicadas increase seed mass or not, then we will use the Wilcoxon rank sum test by using software. The hypotheses will be defined as:

Null hypothesis: There is no difference between them.

Alternative hypothesis: The dead cicadas increase seed masses than the control group.

Thus, the result for the test by using the software is as:

Cicada plants	Control group
0.237	0.212
0.109	0.261
0.261	0.203
0.276	0.215
0.239	0.178
0.238	0.29
0.218	0.268
0.351	0.246
0.317	0.241
0.192	0.188
0.277	0.265
0.209	0.241
0.227	0.285
0.234	0.244
0.266	0.253
0.21	0.19
0.263	0.145
0.245	0.263
0.31	0.135
0.201	0.257
0.241	0.198
0.238	0.19
0.171	0.249
0.255	0.196
0.296	0.247
0.295	0.253
0.305	0.17
0.226	0.155
0.223	0.266
0.211	0.212
0.142	0.253
0.277	0.22
0.235	0.14
0.296
0.217
0.193
0.257
0.276
0.229

Label	Data	Rank
Cicada plants	0.237	34
Cicada plants	0.109	1
Cicada plants	0.261	52.5
Cicada plants	0.276	60.5
Cicada plants	0.239	37
Cicada plants	0.238	35.5
Cicada plants	0.218	26
Cicada plants	0.351	72
Cicada plants	0.317	71
Cicada plants	0.192	13
Cicada plants	0.277	62.5
Cicada plants	0.209	19
Cicada plants	0.227	30
Cicada plants	0.234	32
Cicada plants	0.266	57.5
Cicada plants	0.21	20
Cicada plants	0.263	54.5
Cicada plants	0.245	42
Cicada plants	0.31	70
Cicada plants	0.201	17
Cicada plants	0.241	39
Cicada plants	0.238	35.5
Cicada plants	0.171	8
Cicada plants	0.255	49
Cicada plants	0.296	67.5
Cicada plants	0.295	66
Cicada plants	0.305	69
Cicada plants	0.226	29
Cicada plants	0.223	28
Cicada plants	0.211	21
Cicada plants	0.142	4
Cicada plants	0.277	62.5
Cicada plants	0.235	33
Cicada plants	0.296	67.5
Cicada plants	0.217	25
Cicada plants	0.193	14
Cicada plants	0.257	50.5
Cicada plants	0.276	60.5
Cicada plants	0.229	31
Control group	0.212	22.5
Control group	0.261	52.5
Control group	0.203	18
Control group	0.215	24
Control group	0.178	9
Control group	0.29	65
Control group	0.268	59
Control group	0.246	43
Control group	0.241	39
Control group	0.188	10
Control group	0.265	56
Control group	0.241	39
Control group	0.285	64
Control group	0.244	41
Control group	0.253	47
Control group	0.19	11.5
Control group	0.145	5
Control group	0.263	54.5
Control group	0.135	2
Control group	0.257	50.5
Control group	0.198	16
Control group	0.19	11.5
Control group	0.249	45
Control group	0.196	15
Control group	0.247	44
Control group	0.253	47
Control group	0.17	7
Control group	0.155	6
Control group	0.266	57.5
Control group	0.212	22.5
Control group	0.253	47
Control group	0.22	27
Control group	0.14	3

n	sum of ranks
39	1567	Cicada plants
33	1061	Control group
72	2628	total

1423.50	expected value
88.47	standard deviation
1.62	z, corrected for ties
.0530	p-value (one-tailed, upper)

As we know that if the P-value is less than or equal to the significance level then the null hypothesis is rejected, so we have,

  $P>0.05\Rightarrow \text{Fail to Reject }{H}_0$

Thus, we do not have the sufficient evidence to conclude that dead cicadas increase seed masses than the control group.