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Faculty of Health, Medicine and Life SciencesBBS1003 Syllabus 2020-2021 202020
, Faculty of Health, Medicine and Life Sciences
1.1.1 Seminar 3.1 assignments
Don’t forget watching the videos!
Statistical concepts to be discussed: concept of testing hypotheses, typeI and type II error,
power, p-value
Problem 1
Pete claims he can guess the suit of a randomly selected playing card more than ¼ of the time.
He guesses the symbol of a randomly selected card 100 times and guesses 44 times correct.
The calculated p-value of observing at least 44 correct guessing if the true probability was ¼
is equal to p-value = 0.000027.
Explain why there is strong evidence that Pete can guess the suit correctly more than ¼ of the
time.
Answer:
¼ is equal to 0.25. The hypothesis is that normally the chance of guessing it is equal to 0.25
(true probability). Pete has the alternative which is higher than 0.25. This means:
H0 : π = 0.25
Ha : π > 0.25. (one sided test)
P=0.000027. If the true probability is equal to 0.25, then the probability of guessing at least 44
times correct is equal to 0.000027. This is a very small p-value. The null hypothesis is
rejected which makes the evidence (alternative hypothesis) strong.
Problem 2
A physician measures the blood pressure of 100 randomly selected patients. The observed
average blood pressure was X = 117 mmHg and the population standard deviation was σ=10.
Suppose the following hypothesis is to be tested.
H0 : μ = 120 mmHg versus the alternative
Ha : μ = 115 mmHg. (the equal sign is not a typo)
X−120
The distribution of the test statistic Z = is standard normal distributed (standard
σ /10
normal means: normally distributed with mean 0 and standard deviation equal to 1).
a. Does the distribution refer to the population, sample or sampling distribution (why)?
Sampling distribution; it has a sample mean with a population standard deviation. The
mean is 0 and the standard deviation is 1.
b. How does the distribution of X look like approximately for large samples when the
null-hypothesis is true and how does it look like when the alternative hypothesis is
true (draw these distributions in one figure)?
BBS1003 Syllabus 2020-2021 212121
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