Concept explainers
Develop the appropriate large sample test procedure.
Check whether the plant densities are equal for region 1 and region 2.
Answer to Problem 94SE
The data do not suggest the sufficient result that the plant densities are equal for region 1 and region 2.
Explanation of Solution
Given info:
The data represents the samples taken from the randomly located square sampling quadrate having the area of 1 m2.
Here,
Calculation:
Large sample test procedure:
The estimate of
Here
The estimate of
Here
Then it is assumed that
The variance of
The pooled estimate of
Test statistic:
Here, the sample size is large. That is,
Test procedure:
The aim of the problem is to test the hypotheses that the plant densities are equal for region 1 and region 2.
Assume that the alternative hypothesis as
The mean of the region1 is
The test hypotheses are,
Null hypothesis:
That is, the plant density of region 1 is equal to the density of region 2.
Alternative hypothesis:
That is, the plant density of region 1 is different from the density of region 2.
The value of the
The value of the
The test statistic value is obtained below:
Substitute
Thus, the test statistic value is –5.33.
From Appendix, “Table A.3 Standard Normal Curves”, the standard normal value of –3.40 at 5% level of significance is 0.000.
So, the
The P-value is obtained as given below:
Thus, the P-value is 0.
Decision rule based on P-value approach:
Rejection region for a right-tailed test:
If
If
Conclusion:
Here, the P-value is less than the level of significance.
That is,
Thus, the decision is “reject the null hypothesis”.
Thus, it can be concluded that there is no enough evidence to infer that the plant densities are equal for region 1 and region 2.
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Chapter 9 Solutions
Probability and Statistics for Engineering and the Sciences
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