Other
Experimental Design and Analysis - Practise Exam with answers
- Course
- Institution
A practise exam with answers for the course Experimental Design and Analysis, MSc AI.
[Show more]
Seller
Follow
tararoopram
Content preview
Question 1Birthweights a) The vector birthweight contains the birthweights (in grams) of 188 newborn
babies. Denote the underlying mean birthweight by μ. Suppose we implemented the following
commands in R:
> mean(birthweight)
2913.293
> var(birthweight)
486506.6
> qnorm(0.96)
1.750686
> qnorm(0.98)
2.053749
Assuming normality, construct a bounded 96% confidence interval (CI) for μ:
[2805, 3010.4] - [2806.19, 3015.5] - [2808.08, 3018.5] - [2800.19, 3011.5]
. Evaluate the sample size needed to provide that the length of the 96%-CI is at most 100:
830 - 813 - 798 - 821 - 578
. Would it be possible to compute a bootstrap 92%-CI for μ by using the sample birthweights?
Not relevant - yes - no
Question 2
Birthweights b) The vector birthweight contains the birthweights (in grams) of 188 newborn
babies. Denote the underlying mean birthweight by μ. An expert claims that the mean
birthweight is bigger than 2800 gram. We want to verify this claim by using relevant test(s).
Choose the correct claim(s).
We can use the following sign test
binom.test(sum(birthweight<=2800),n,0.5,alt="l").
We can use the following sign test
binom.test(sum(birthweight>2800),n,0.5,alt="g").
Under normality, we can use the following t-test t.test(birthweight,mu=2800,alt="l")
Under normality, we can use the following t-test
t.test(birthweight,mu=2800,alt="g")
We cannot perform a sign tests for this problem.
We can use the following sign test binom.test(sum(birthweight<2800),n,0.5,alt="g").
Question 3
Birthweights c) The vector birthweight contains the birthweights (in grams) of 188 newborn
babies. Denote the underlying mean birthweight by μ. An expert claims that the mean
birthweight is bigger than 2800 gram. We want to verify this claim by using relevant test(s).
Suppose we have two tests to verify the claim of the expert. One test has the significance
alpha=0.3 and the power 0.78, the second test has the significance alpha=0.4 and the error of
the second kind 0.25. Which of the two tests is preferable?
, 1st - 2nd - cannot say
.
Suppose we use a t-test to verify the claim of the expert, then
We can estimate - we cannot estimate - we can compute
its power for
All parameter values from the null hypothesis - All parameter values - All parameter values
from the alternative hypothesis
.
Question 4
Birthweights d) The vector birthweight contains the birthweights (in grams) of 188 newborn
babies. Let p be the probability that birthweight of a newborn baby is less than 2600 gram.
Suppose we implemented the following command in R:
> p=sum(t<2600)/n; p
0.3522727
Suppose further that, using asymptotic normality, the expert computed the left end pl=0.25 of
the confidence interval [pl,pr] for p. We recover the whole confidence interval as
[0.15, 0.39] - [0.25, 0.41] - [0.23, 0.45] - [0.19, 0.44]
(rounded to two decimal digits) and its confidence level we recover as
q=(p+0.25)/sqrt(p*(1-p)/n); 1-2*(1-pnorm(q))
q=(p+0.25)/sqrt(p*(1-p)/n); 1-2*(1-qnorm(q))
q=(p-0.25)/sqrt(p*(1-p)/n); 1-(1-pnorm(q))
q=(p-0.25)/sqrt(p*(1-p)/n); 1-2*(1-pnorm(q))
Question 5
Birthweights e) The vector birthweight contains the birthweights (in grams) of 188 newborn
babies. An expert reports that there were 34 male and 28 female babies among 62 who
weighted less than 2600 gram, and 61 male and 65 female babies among the remaining 126
babies. The expert claims that the mean weight is different for male and female babies. We
want to verify this claim by an appropriate test. To test the claim, represent the data in the form
of contingency table.
male female
weight<2600g V1 V2
weight>2600g V3 V4
Determine the values of the above contingency table.
V1= 28 - 61 - 65 - 68 - 34
V2= 28 - 61 - 65 - 68 - 34
V3= 28 - 61 - 65 - 68 - 34
V4= 28 - 61 - 65 - 68 - 34
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller tararoopram. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for $8.49. You're not tied to anything after your purchase.
Can Stuvia be trusted?
4.6 stars on Google & Trustpilot (+1000 reviews)
48072 documents were sold in the last 30 days
Founded in 2010, the go-to place to buy study notes for 15 years now