A statistical program is recommended. A random sample of soil specimens was obta

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 1.12 5.09 0.97 1.59 4.60 0.32 0.55 1.45 0.14 4.47 1.20 3.50 5.02 4.67 5.22 2.69 3.93 3.17 3.03 2.21 0.69 4.47 3.31 1.17 0.74 117 1.572.62 1.66 2.05 The values of the sample mean, sample standard deviation, and (estimated) standard error of the mean are 2.480, 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 Ho: = 3 Ha: > 3 Ha:

Explanation / Answer

Given that,
population mean(u)=3
sample mean, x =2.48
standard deviation, s =1.614
number (n)=30
null, Ho: =3
alternate, H1: !=3
level of significance, = 0.1
from standard normal table, two tailed t /2 =1.699
since our test is two-tailed
reject Ho, if to < -1.699 OR if to > 1.699
we use test statistic (t) = x-u/(s.d/sqrt(n))
to =2.48-3/(1.614/sqrt(30))
to =-1.7647
| to | =1.7647
critical value
the value of |t | with n-1 = 29 d.f is 1.699
we got |to| =1.7647 & | t | =1.699
make decision
hence value of | to | > | t | and here we reject Ho
p-value :two tailed ( double the one tail ) - Ha : ( p != -1.7647 ) = 0.0882
hence value of p0.1 > 0.0882,here we reject Ho
ANSWERS
---------------
test statistic: -1.76
p-value: 0.088

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