The historical mean yield of soybeans from farms in Indiana is 31.9 bushels per
ID: 2925939 • Letter: T
Question
The historical mean yield of soybeans from farms in Indiana is 31.9 bushels per acre. Following a recent dry summer, a random sample of 26 farms from across the state was obtained. The sample mean yield in bushels per acre was 30.088 with a sample standard deviation of 4.433. Is there any evidence to suggest that the lack of rain adversely affected the soybean yield in Indiana?
What is the population of interest?
Was the sample collected randomly? What does that imply in terms of the conclusions we draw?
What is the variable? Is it categorical or quantitative?
In words, what is the parameter of interest? What symbol do we use for this parameter?
In symbols, what are the researchers’ hypotheses?
What is the sample statistic? What symbol do we use for this?
Is the validity condition for the Theory Based Approach met for this situation? Why or why not?
Using the Theory Based Approach, what is the standard error? (Show your work).
Using the result from problem 8, what is our standardized statistic? (show your work)
What can you conclude, in context, based on your standardized statistic in problem 9?
The Theory-based p-value was found to be 0.0238. Using = 0.05, what can you conclude? Make sure your conclusion is in context!
What type of error could you have made in this scenario? Write the error in context.
Explanation / Answer
Given that,
population mean(u)=31.9
standard deviation, =4.433
sample mean, x =30.088
number (n)=26
null, Ho: =31.9
alternate, H1: !=31.9
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 = 30.088-31.9/(4.433/sqrt(26)
zo = -2.08424
| zo | = 2.08424
critical value
the value of |z | at los 5% is 1.96
we got |zo| =2.08424 & | z | = 1.96
make decision
hence value of | zo | > | z | and here we reject Ho
p-value : two tailed ( double the one tail ) - ha : ( p != -2.08424 ) = 0.03714
hence value of p0.05 > 0.03714, here we reject Ho
ANSWERS
---------------
null, Ho: =31.9
alternate, H1: !=31.9
test statistic: -2.08424
critical value: -1.96 , 1.96
decision: reject Ho
p-value: 0.03714
What is the population of interest?
mean rate of rain adversely affected the soybean yield in Indiana
Was the sample collected randomly? What does that imply in terms of the conclusions we draw?
yes
What is the variable? Is it categorical or quantitative?
quantitative
In symbols, what are the researchers’ hypotheses?
null,the lack of rain does n't effect the soybean yield in Indiana, Ho: =31.9
alternate, the lack of rain adversely affected the soybean yield in Indiana, H1: !=31.9
What is the sample statistic? What symbol do we use for this?
-2.08424
Using the Theory Based Approach, what is the standard error? (Show your work).
stanadard error = sd/ sqrt(n)
where,
sd = population standard deviation
n = population size
stanadard error = ( 4.433/ sqrt ( 26) )
= 0.869
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