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TUT 1 on Chapter 18 (linked to Ch 9 &10) Preparation
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
b) Give the value of the Sign test statistic:
c) Specify the exact distribution of 𝑥 𝑢𝑛𝑑𝑒𝑟 𝐻 :
d) Define the p-value and calculate it by using the Excel function BINOM.DIST:
e) Interpret the p-value and make a conclusion:
Question 2
The median number of part-time employees at fast-food restaurants in a particular city was
known to be at most 18 last year. City officials think the use of part-time employees may be
increasing.
A sample of 22 fast-food restaurants showed that 17 restaurants were employing more
than 18 part-time employees, 2 restaurants were employing exactly 18 part-time
employees, and 3 restaurants were employing fewer than 18 part-time employees.
Can it be concluded that the median number of part-time employees has increased? Use
the sign test and test, on a 5% level.
a) Sample size for the sign test
b) Hypotheses:
c) Value of the Sign test statistic:
d) Specify the exact distribution of 𝑋 𝑢𝑛𝑑𝑒𝑟 𝐻 :
e) Write down the normal approximation to this binomial distribution:
f) Calculate this one-sided p-value by using the Excel function NORM.S.DIST
g) Decision:
h) Conclusion:
TUT 1 on Chapter 18 (linked to Ch 9 &10) Preparation
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
b) Give the value of the Sign test statistic:
c) Specify the exact distribution of 𝑥 𝑢𝑛𝑑𝑒𝑟 𝐻 :
d) Define the p-value and calculate it by using the Excel function BINOM.DIST:
e) Interpret the p-value and make a conclusion:
Question 2
The median number of part-time employees at fast-food restaurants in a particular city was
known to be at most 18 last year. City officials think the use of part-time employees may be
increasing.
A sample of 22 fast-food restaurants showed that 17 restaurants were employing more
than 18 part-time employees, 2 restaurants were employing exactly 18 part-time
employees, and 3 restaurants were employing fewer than 18 part-time employees.
Can it be concluded that the median number of part-time employees has increased? Use
the sign test and test, on a 5% level.
a) Sample size for the sign test
b) Hypotheses:
c) Value of the Sign test statistic:
d) Specify the exact distribution of 𝑋 𝑢𝑛𝑑𝑒𝑟 𝐻 :
e) Write down the normal approximation to this binomial distribution:
f) Calculate this one-sided p-value by using the Excel function NORM.S.DIST
g) Decision:
h) Conclusion:
