Question

1. The numbers below represent heights (in feet) of 3-year old elm trees. 5.1, 5.5, 5.8, 6.1, 6.2, 6.4, 6.7, 6.8, 6.9, 7.0,
7.2, 7.3, 7.3, 7.4, 7.5, 7.7, 7.9, 8.1, 8.1, 8.2,
8.3, 8.5, 8.6, 8.6, 8.7, 8.7, 8.9, 8.9, 9.0, 9.1,

9.3, 9.4, 9.6, 9.8, 10.0, 10.2, 10.2

Using the chi-square goodness-of-fit test, determine whether the heights of 3-year old elm trees are normally distributed, at the a = .05 significance level. Also, find the p- value.

Answer 1

The hypothesis being tested is:

H₀: The heights of 3-year old elm trees are not normally distributed

H_a: The heights of 3-year old elm trees are normally distributed

The output is:

observed	expected	O - E	(O - E)² / E	% of chisq
5.1	7.973	-2.873	1.035	12.58
5.5	7.973	-2.473	0.767	9.32
5.8	7.973	-2.173	0.592	7.20
6.1	7.973	-1.873	0.440	5.35
6.2	7.973	-1.773	0.394	4.79
6.4	7.973	-1.573	0.310	3.77
6.7	7.973	-1.273	0.203	2.47
6.8	7.973	-1.173	0.173	2.10
6.9	7.973	-1.073	0.144	1.75
7	7.973	-0.973	0.119	1.44
7.2	7.973	-0.773	0.075	0.91
7.3	7.973	-0.673	0.057	0.69
7.3	7.973	-0.673	0.057	0.69
7.4	7.973	-0.573	0.041	0.50
7.5	7.973	-0.473	0.028	0.34
7.7	7.973	-0.273	0.009	0.11
7.9	7.973	-0.073	0.001	0.01
8.1	7.973	0.127	0.002	0.02
8.1	7.973	0.127	0.002	0.02
8.2	7.973	0.227	0.006	0.08
8.3	7.973	0.327	0.013	0.16
8.5	7.973	0.527	0.035	0.42
8.6	7.973	0.627	0.049	0.60
8.6	7.973	0.627	0.049	0.60
8.7	7.973	0.727	0.066	0.81
8.7	7.973	0.727	0.066	0.81
8.9	7.973	0.927	0.108	1.31
8.9	7.973	0.927	0.108	1.31
9	7.973	1.027	0.132	1.61
9.1	7.973	1.127	0.159	1.94
9.3	7.973	1.327	0.221	2.68
9.4	7.973	1.427	0.255	3.10
9.6	7.973	1.627	0.332	4.03
9.8	7.973	1.827	0.419	5.09
10	7.973	2.027	0.515	6.26
10.2	7.973	2.227	0.622	7.56
10.2	7.973	2.227	0.622	7.56
295	295.000	0.000	8.229	100.00
8.23	chi-square
36	df
1.0000	p-value

The p-value from the output is 1.0000.

Since the p-value (1.0000) is greater than the significance level (0.05), we cannot reject the null hypothesis.

Therefore, we can conclude that the heights of 3-year old elm trees are normally distributed.

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