2) Experience of potato farmers in a certain region of the country is that the e

Question

2) Experience of potato farmers in a certain region of the country is that the expected potato yield is 40 t/ha (tonnes per hectare) with standard deviation 1.5 tha. A particular farm is studied and each of5 different hectares on the farm are observed to have yields of40.71, 39.44, 40.36, 39.98, and 40.58. Assume that the standard deviation given above holds at this farm. a) Does the evidence suggest that the yield is not 40 t/ha at this farm? Test at a significance level of 590 b) What is the p-value for this test?

Explanation / Answer

Given that,
population mean(u)=40
standard deviation, =1.5
sample mean, x =40.214
number (n)=29
null, Ho: =40
alternate, H1: !=40
level of significance, = 0.05
from standard normal table, two tailed z /2 =1.96
since our test is two-tailed
reject Ho, if zo < -1.96 OR if zo > 1.96
we use test statistic (z) = x-u/(s.d/sqrt(n))
zo = 40.214-40/(1.5/sqrt(29)
zo = 0.77
| zo | = 0.77
critical value
the value of |z | at los 5% is 1.96
we got |zo| =0.77 & | z | = 1.96
make decision
hence value of |zo | < | z | and here we do not reject Ho
p-value : two tailed ( double the one tail ) - ha : ( p != 0.77 ) = 0.44
hence value of p0.05 < 0.44, here we do not reject Ho
ANSWERS
---------------
null, Ho: =40
alternate, H1: !=40
test statistic: 0.77
critical value: -1.96 , 1.96
decision: do not reject Ho
p-value: 0.44

we have evidence that yield value is 40

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