rainforest oil palrm plantatioNote that the mean flux value |0.05 1 ±0.040 mean
ID: 3306548 • Letter: R
Question
rainforest oil palrm plantatioNote that the mean flux value |0.05 1 ±0.040 mean nux of nitrogen.| 0.036±0.041 from soil (mg N/m2 hr) number of of nitrogen from soil is expressed as the mean plus or minus one standard deviation. 89 101 nents Calculate the tvalue to compare these two means. Assume the population standard deviation for each data set is the same Number 1c ale = 11 2.545 At which of the confidence levels are the results different? A list of Student's t values can be found in this table. 90% 95% 98% 99% 99.5% 99.9%Explanation / Answer
Solution:-
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: 1 - 2 = 0
Alternative hypothesis: 1 - 2 0
Note that these hypotheses constitute a two-tailed test. The null hypothesis will be rejected if the difference between sample means is too big or if it is too small.
Formulate an analysis plan. For this analysis, the significance level is 0.05. Using sample data, we will conduct a two-sample t-test of the null hypothesis.
Analyze sample data. Using sample data, we compute the standard error (SE), degrees of freedom (DF), and the t statistic test statistic (t).
SE = sqrt[(s12/n1) + (s22/n2)]
SE = 0.005893
DF = 89 + 101 - 2
D.F = 188
t = [ (x1 - x2) - d ] / SE
t = - 2.545
where s1 is the standard deviation of sample 1, s2 is the standard deviation of sample 2, n1 is the size of sample 1, n2 is the size of sample 2, x1 is the mean of sample 1, x2 is the mean of sample 2, d is the hypothesized difference between the population means, and SE is the standard error.
Since we have a two-tailed test, the P-value is the probability that a t statistic having 188 degrees of freedom is more extreme than - 2.545; that is, less than -2.545 or greater than 2.545.
Thus, the P-value = 0.01173
Interpret results. Since the P-value (0.01173) is less than the significance level (0.10, 0.05 and 0.02), we cannot accept the null hypothesis.
The results are different at confidence interval 90%, 95% and 98%.