A farmer wants to know whether a new fertilizer has increased the mean weight of his apples. With the old fertilizer, the mean weight was 4.0 ounces per apple. The farmer decides to test $$\(\mathrm{H}_{0}: \mu=4.0\)$$ ounces versus $$\(\mathrm{H}_{a}: \mu> 4.0\)$$ ounces, at a $$\(5 \%\)$$ level of significance, where $$\(\mu=\)$$ the mean weight of apples using the new fertilizer. The weights of apples are approximately normally distributed. The farmer takes a random sample of 16 apples and computes a mean of 4.3 ounces and a standard deviation of 0.6 ounces. Which of the following gives the $$\(p\)$$-value for this test?
A.
\(P(Z> 2)\)
B.
\(P(Z< 2)\)
C.
\(\quad P(t> 2)\) with 15 degrees of freedom
D.
\(\quad P(t< 2)\) with 15 degrees of freedom
E.
\(\quad P(t> 2)\) with 16 degrees of freedom
Exam No：AP Statistics Problem Set 11 Year：2024 Question No：APStatistics2024AP0450
Answer:
C
Knowledge points:
5.7 Sampling Distributions for Sample Means
7.4 Setting Up a Test for a Population Mean
7.5 Carrying Out a Test for a Population Mean
Solution:
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