The yield of apples from apple trees is normally distributed. A farmer knows that she will be able to fulfill all her or
Posted: Mon May 09, 2022 1:01 pm
The yield of apples from apple trees is normally distributed. A
farmer knows that she will be able to fulfill all her orders if the
average yield from her apple trees is greater than 115 kilograms,
and so wants to test that hypothesis. The farmer observed a simple
random sample of 25 trees from her orchard and found the mean yield
was 119 kilograms with a sample standard deviation of 14 kilograms.
The level of significance (alpha) used for this problem is
0.05.
a) State the pair of hypotheses using proper notation and
mathematical symbols for testing the farmer's test as stated
above.
b) What are the assumptions required to be valid for the
hypothesis test to be valid? Note: When making a statement
involving the random variable, it must be put in actual context and
be specific.
c) What is the appropriate test statistic? Show work that
includes the appropriate formula and how the values provided fit
into that formula. Give your final answer an appropriate label.
d) Find/calculate the P-value for this hypothesis test. If using
the calculator, show full calculator syntax. If using another
method, describe your process.
e) What is the decision (Reject Ho or Fail to Reject Ho (Retain
Ho)? Give full supporting statistical reasoning to your decision by
comparing the two appropriate values necessary.
f) Give the statistical and real-world conclusions corresponding
this hypothesis test and put in context to the random variable
involved.
farmer knows that she will be able to fulfill all her orders if the
average yield from her apple trees is greater than 115 kilograms,
and so wants to test that hypothesis. The farmer observed a simple
random sample of 25 trees from her orchard and found the mean yield
was 119 kilograms with a sample standard deviation of 14 kilograms.
The level of significance (alpha) used for this problem is
0.05.
a) State the pair of hypotheses using proper notation and
mathematical symbols for testing the farmer's test as stated
above.
b) What are the assumptions required to be valid for the
hypothesis test to be valid? Note: When making a statement
involving the random variable, it must be put in actual context and
be specific.
c) What is the appropriate test statistic? Show work that
includes the appropriate formula and how the values provided fit
into that formula. Give your final answer an appropriate label.
d) Find/calculate the P-value for this hypothesis test. If using
the calculator, show full calculator syntax. If using another
method, describe your process.
e) What is the decision (Reject Ho or Fail to Reject Ho (Retain
Ho)? Give full supporting statistical reasoning to your decision by
comparing the two appropriate values necessary.
f) Give the statistical and real-world conclusions corresponding
this hypothesis test and put in context to the random variable
involved.