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 â€“ 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 â€“ 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: â€œThe 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: â€œThe 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