Sub: Statistics Topic: Testing
Question:
At the beginning of the course of Statistical Methods I, the instructor recommended that
students devote 3 hours per week for the duration of the 13-week semester, for a total of 39
hours.
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It is known that the time spent on studying statistics follow a normal distribution. Throughout
the course duration, students were claiming that they were following the instructor’s
recommendation. At the course completion, a random sample of 10 students enrolled in the
course was drawn where each student was asked how many hours he or she spent doing
homework in statistics. The data are listed below:
45 38 37 40 44 38 46 37 42 43
Formulate a suitable null and alternative hypothesis to test the students’ claim that they
followed their instructor’s recommendation at a 5% level of significance and interpret your
findings.
Solution:
Hypotheses:
Null Hypothesis: H0: 1 39
That is, H0: The mean time spent by students during the examination is equal to 39 hours.
Alternative Hypothesis: Ha: 1 2
The mean time spent by students during the examination is not equal to 39 hours.
Level of Significance: α = 0.05
Test Statistic:
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Sub: Statistics Topic: Testing
Since the sample sizes n = 10 which is less than 30, we use the small sample test (that is
student - t-test)
The test statistic is given by
t=
=
=
=
= 1.843
Hence the calculated test statistic is 1.843
Critical value:
Since the test statistic value (t= 1.849) is lesser than the critical value ( 2.2622), we
do not reject the null hypothesis at 5 % level of significance.
** End of the Solution **
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*The Homework solutions from ClassOf1 are intended to help the student understand the approach to solving the problem and not for submitting
the same in lieu of your academic submissions for grades.