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I have a problem about the hypothesis testing and decision making as follows:

A botanist wishes to test the null hypothesis that the average diameter of the flowers of a particular plant is 9.6cm. He decides to take a random sample of size $n$=80 and accept the null hypothesis if the mean of the sample falls between 9.3cm and 9.9cm; if the mean of this sample falls outside this interval, he will reject the null hypothesis. What decision will he make and will it be in error if
(a) he gets a sample mean of 10.2cm and $\mu$=9.6cm;
(b) he gets a sample mean of 10.2cm and $\mu$=9.8cm;
(c) he gets a sample mean of 9.2cm and $\mu$=9.6cm;
(d) he gets a sample mean of 9.2cm and $\mu$=9.8cm.

Does anyone have an idea how to deal with this problem? I just do not so understand what the problem asks for and how to approach it. Many thanks!

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1 Answer 1

This is essentially a vocabulary test. No calculation necessary!

(a) He will reject the null hypothesis, since $10.2$ is outside the range he has set. Since $\mu$ is in fact $9.6$, he will be mistaken.

(b) He will reject the null hypothesis, for the same reason as above. Since $\mu\ne 9.6$, he will be right.

You can do the others.

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