Problem 1:
A student is studying for the test which has 40 questions. Each
question is a multiple choice question with 6 options. The student
studied 25% of the content of the test. The rest of the test he
will randomly pick the answer. We assume that students answered
correctly al the questions he or she studied.
1. Find PScore=5.
2. Find PScore=30.
3. Find PScore=k.
4. What should the student expect to be his score on the
test?
5. Another student scored 25 on the test. What is the expected
value of the material the student studied?
6. 100 students took the test. The average test score was 30
with standard deviation of 4. Find 95% confidence intervalfor the
amount of material (in percentage) the students studied?
Problem 2.
A sanitary inspection visit 5 restaurants on 10 different
occasions. It graded them on the scale 0 – 100. A company is using
these scores to determine whether any of the restaurants need to
improve. Which tool you would suggest to the company to see whether
there is any difference between the sanitary score of the five
restaurants?
a) Confidence Intervals
b) ANOVA
c) Correlation Matrix
d) Linear Regression
e) Histograms
f) CATNAP
Problem 3. We would like to use SAT scores to predict students
success in their first Math Course. Which tool should we use?
a) Confidence Intervals
b) ANOVA
c) Correlation Matrix
d) Linear Regression
e) Histograms
f) CATNAP
Problem 4
This is the outcome of the ANOVA test on the production data of
five factories R1 – R5. Research questions is to find which factory
or factories have the best production?
(A) Write the Null-Hypothesis.
(B) Write a report.
(C) Do we know as a result of ANOVA test which factory or
factories have the largest production or we need to do the
follow-up tests? If we do need the follow-up tests which ones?
Explain in no more than 3 lines.
Problem 5.
The statement in a report says: “The linear model is a good fit
to the dataâ€. This statement should be supported by one of the
following numbers:
a) p-value = 0.0343
b) R-Sq = 0.872
c) R-Sq < 0.0001
d) p-value = 0.927
e) SSB = 123.45
f) F stat = 123.45
Problem 6.
The statement in a report says: “The regression results have
been statistically significant.â€. This statement should be
supported by one of the following numbers:
a) p-value = 0.0343
b) R-Sq = 0.872
c) R-Sq < 0.0001
d) p-value = 0.927
e) SSB = 123.45
f) F stat = 123.45
Problem 7
A swimming coach has been taking attendance at the outdoor
swimming pool practices. He asked the following research question:
Could I predict the number of swimmers attending the practice from
the dailytemperature(measured in F)? We run linear regression and
here are the results:
Write a short report.
Assume the model is a good fit. For each increase in temperature
by 10F what is the predicted increase in number of swimmers?
Problem 8.
A correlation matrix is given.
1. Which two variables are correlated the most?
2. Sketch the correlation relationship between R4 and R5. Be
precise as possible!
Problem 9
(A) A sample of blood has been drawn from 100 randomly chosen
people. We tested their cholesterol levels. The mean was 189 with
standard deviation of 23. Compute the 99%CI for the population
mean.
(B) If in the problem above we increase the confidence level the
corresponding interval would:
(a) shrink
(b) stay the same
(c) get wider
(d) depends
(e) none of the above
(C) Assume that 99% CI is [ 150, 210] and we quadruple the
sample size the corresponding confidence interval would be:
(a) [130, 230]
(b) stay the same
(c) [172.5, 187.5]
(d) depends
(e) [ 165, 195]
(D) If in the problem A the sample consists of 12 samples then
we would use which one of the distributions from the list below to
compute the 99%CI.
(a) z-distribution
(b) normal distribution with mean 12 and standard deviation of
1
(c) t-distribution with 12 degrees of freedom
(d) beta distribution with 12 degrees of freedom
(e) t-distribution with 11 degrees of freedom
(f) none of the above
