han 30. He would like to colle atistical hypothesis testing. e ACT score of the students

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A professor believes that his students mean ACT scores are not
lower than 30. He would like to collect evidence of his claim and
do a statistical hypothesis testing. The data center director said
that the ACT score of the students follows a normal distribution
with variance of value 9.
(a) Write down the null (Ho) and alternative (H;) hypotheses
based on his claim. Is the claim a Ho or H, claim? Is this a
left-tailed, right-tailed, or two-tailed test? Please explain.
(b) Due to research budget cut, the professor's assistant
can only collect a small random sample of size 16. Are one-
sample z-test and/or t-test procedures appropriate under
such a small size? If yes, why? If not, add conditions to
make the procedures appropriate.
(c) The assistant only remembers that the professor said
28.7 is the critical value to be compared with the observed
sample mean x. Please help her decide the rejection region.
Transcribed Image Text:A professor believes that his students mean ACT scores are not lower than 30. He would like to collect evidence of his claim and do a statistical hypothesis testing. The data center director said that the ACT score of the students follows a normal distribution with variance of value 9. (a) Write down the null (Ho) and alternative (H;) hypotheses based on his claim. Is the claim a Ho or H, claim? Is this a left-tailed, right-tailed, or two-tailed test? Please explain. (b) Due to research budget cut, the professor's assistant can only collect a small random sample of size 16. Are one- sample z-test and/or t-test procedures appropriate under such a small size? If yes, why? If not, add conditions to make the procedures appropriate. (c) The assistant only remembers that the professor said 28.7 is the critical value to be compared with the observed sample mean x. Please help her decide the rejection region.
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