A statistical program is recommended A random sample of soil specimens was obtai

Question

A statistical program is recommended A random sample of soil specimens was obtained, and the amount of organic matter (%) in the soil was determined for each specimen, resulting in the accompanying data 1.11 5.09 0.97 1.59 4.60 0.32 0.SS 1.45 0.18 4.47 1.20 3.50 5.02 4.67 5.22 2.69 3.99 3.17 3.03 2.21 0.69 4.47 3.31 1.17 0.75 1.17 1.57 2.62 1.66 2.05 The values of the sample mean, sample standard deviation, and (estimated) standard error of the mean are 2.483, 1.614, and 0.295, respectively. Does this data suggest that the true average percentage of organic matter in such soil is something other than 3%? Carry out a test of the appropriate hypotheses at significance level 0.10 Note: A normal probability plot of the data shows an acceptable pattern in light of the reasonably large sample size.] State the appropriate hypotheses. Ha: -3 Ha: 3 Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to three decimal places.) t1.754 p-value= 1.96 What can you conclude?

Explanation / Answer

Here we are given a sample size of 30. Therefore for n-1 = 29 degrees of freedom, and as this is a two tailed test, the p-value here is computed as:

p = 2P(t29 < -1.754 )

Getting the above probability from the t-distribution tables, we get:

p = 2P(t29 < -1.754 )=2*0.045 = 0.090

Therefore 0.090 is the required p-value here.

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