1
TUT 1 on Chapter 18 (linked to Ch 9 &10) Preparation MEMO
Question 1
The computer laboratory where students do their practical tests is undecided whether to
increase or decrease the capacity of the laboratory. From past experience they know that
the median number of students who do their practical tests per session is 80.
A simple random sample of 10 sessions is taken to test the hypothesis.
88 90 82 81 86 78 76 92 80 84
Use the exact sign test to test at a 5% level of significance that the median number of
students per session is different from 80 students.
a) Formulate the hypotheses
𝐻 : population median = 80
𝐻 : population median 80
b) Give the value of the Sign test statistic:
𝑥 number of positive signs 7
Sample size decreases from 10 to 𝑛 9 since there is a tie on one sample value.
c) Specify the exact distribution of 𝑥 𝑢𝑛𝑑𝑒𝑟 𝐻 :
𝑥~𝑏𝑖𝑛𝑜𝑚𝑖𝑎𝑙 9 ; 0.5
d) Define the p-value and calculate it by using the Excel function BINOM.DIST:
one-sided p-value 𝑃 𝑥 𝑡𝑒𝑠𝑡 𝑠𝑡𝑎𝑡𝑖𝑠𝑡𝑖𝑐
𝑃 𝑥 7
1 𝑃 𝑥 6
1 BINOM. DIST 6, 9 ,0.5, TRUE
1 0.9102
0.0898
two-sided p-value = 2 * 0.0898 = 0.1796
e) Interpret the p-value and make a conclusion:
p-value (= 0.1796) 𝛼 (= 0.05) ⇒ 𝐻 can not be rejected
Conclusion:
The population median number of students per session is not significantly different
from 80 at the 5% level of significance.
TUT 1 on Chapter 18 (linked to Ch 9 &10) Preparation MEMO
Question 1
The computer laboratory where students do their practical tests is undecided whether to
increase or decrease the capacity of the laboratory. From past experience they know that
the median number of students who do their practical tests per session is 80.
A simple random sample of 10 sessions is taken to test the hypothesis.
88 90 82 81 86 78 76 92 80 84
Use the exact sign test to test at a 5% level of significance that the median number of
students per session is different from 80 students.
a) Formulate the hypotheses
𝐻 : population median = 80
𝐻 : population median 80
b) Give the value of the Sign test statistic:
𝑥 number of positive signs 7
Sample size decreases from 10 to 𝑛 9 since there is a tie on one sample value.
c) Specify the exact distribution of 𝑥 𝑢𝑛𝑑𝑒𝑟 𝐻 :
𝑥~𝑏𝑖𝑛𝑜𝑚𝑖𝑎𝑙 9 ; 0.5
d) Define the p-value and calculate it by using the Excel function BINOM.DIST:
one-sided p-value 𝑃 𝑥 𝑡𝑒𝑠𝑡 𝑠𝑡𝑎𝑡𝑖𝑠𝑡𝑖𝑐
𝑃 𝑥 7
1 𝑃 𝑥 6
1 BINOM. DIST 6, 9 ,0.5, TRUE
1 0.9102
0.0898
two-sided p-value = 2 * 0.0898 = 0.1796
e) Interpret the p-value and make a conclusion:
p-value (= 0.1796) 𝛼 (= 0.05) ⇒ 𝐻 can not be rejected
Conclusion:
The population median number of students per session is not significantly different
from 80 at the 5% level of significance.
