Five years ago, 10.4% of high school students had tried marijuana for the first
ID: 3319608 • Letter: F
Question
Five years ago,
10.4% of high school students had tried marijuana for the first time before the age of 13. A school resource officer (SRO) thinks that the proportion of high school students who have tried marijuana for the first time before the age of 13 has decreased
since then.
(a) Determine the null and alternative hypotheses. Which of the following is correct?
A. Upper H 0H0:p=0.1040.104;Upper H 1H1:p 0.1040.104
B. Upper H 0H0:p=0.1040.104;Upper H 1H1:pless than<0.1040.104
C.Upper H 0H0:pequals=0.1040.104;Upper H 1H1:pgreater than>0.1040.104
(b) Suppose sample data indicate that the null hypothesis
should notshould not
be rejected. State the conclusion of the researcher.
A.
There
is notis not
sufficient evidence to conclude that the proportion of high school students has stayed the same.
B.
There
is notis not
sufficient evidence to conclude that the proportion of high school students has
decreaseddecreased.
C.
There
isis
sufficient evidence to conclude that the proportion of high school students has stayed the same.
D.
There
isis
sufficient evidence to conclude that the proportion of high school students has
decreaseddecreased.
(c) Suppose, in fact, that the proportion of high school students who have tried marijuana before the age of 13 was
10.110.1%.
Was a type I or type II error committed?
A.
The SRO committed a type
IIII
error because he
did not rejectdid not reject
the null hypothesis
whenwhen
thethe
alternativealternative
hypothesishypothesis
is true.
B.
The SRO committed a type
IIII
error because he
acceptedaccepted
the null hypothesis
whenwhen
thethe
alternativealternative
hypothesishypothesis
is true.
C.
The SRO committed a type
Upper II
error because he
did not rejectdid not reject
the null hypothesis
whenwhen
thethe
alternativealternative
hypothesishypothesis
is true.
D.
The SRO committed a type
Upper II
error because he
acceptedaccepted
the null hypothesis
whenwhen
thethe
alternativealternative
hypothesishypothesis
is true.
Explanation / Answer
(a) The null and alternative hypotheses are:
H0: p = 0.104 against H1: p < 0.104.
Hence, Option (B) is the correct choice. (Ans).
(b) If the null hypothesis is not rejected, then the conclusion
will be: There is not sufficient evidence to conclude that the
proportion of high school students has decreased.
Hence, Option (B) is the correct choice. (Ans).
(c) Here, the SRO committed Type-II error since he did not
reject the null hypothesis when the alternative hypothesis is
true. Hence, Option (A) is the correct choice. (Ans).
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