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You have been asked to calculate a 95% confidence interval for a data sample.

INSTRUCTIONS TO CANDIDATES
ANSWER ALL QUESTIONS

QUESTION 1

  1. You have been asked to calculate a 95% confidence interval for a data sample.  You know the mean of this sample but you do not know the population standard deviation.  The probability distribution you should use in your calculations is the

 

 

Whatever distribution the data follow.

 

 

Normal Distribution.

 

 

no distribution.  You cannot do this problem. 

 

 

Student-t Distribution.

QUESTION 2

  1. Using the data below, calculate the 95% confidence interval.  Round your answers to two decimal places.  What is the lower bound for the confidence interval?

3.3

2.9

3

3.1

2.7

2.6

4

3.8

2.8

3.6

 

QUESTION 3

  1. Calculate the 95% confidence interval for the data below.  Round your answers to two decimal places.  What is the upper bound for the 95% confidence interval?

3.3

2.9

3

3.1

2.7

2.6

4

3.8

2.8

3.6

 

QUESTION 4

  1. Calculate a 90% confidence for the data below.  Round your answers to two decimal places.  What is the lower bound on the 90% confidence interval? 

3.3

2.9

3

3.1

2.7

2.6

4

3.8

2.8

3.6

 

QUESTION 5

  1. You have been asked to calculate a 90% confidence interval for the data below.  Round your answers to two decimal places.  What is the upper bound on the 90% confidence interval?

3.3

2.9

3

3.1

2.7

2.6

4

3.8

2.8

3.6

QUESTION 6

  1. The 90% confidence interval is wider than the 95% confidence interval for the same data because a lower confidence level actually covers more area, i.e. a wider interval. 
     True
     False

QUESTION 7

  1. If you increase the number of observations in your dataset you would expect your confidence interval to become narrower. 
     True
     False

QUESTION 8

  1. Many students misinterpret a confidence interval, i.e. a 90% confidence interval, to mean that there is confidence that 90% of the data lie within this interval.  That is not true.  Fill in the blank in the following sentence to complete what is accurately meant in expressing a confidence interval for an analysis involving the true population mean of students' GPA.
    We estimate with 90% confidence that ________ lies between the lower bound of the confidence interval and the upper bound of the confidence interval.

QUESTION 9

    1. Fill in the blanks in the following sentences about the differences between the Normal distribution and the Student-t distribution. 
      The Student-t distribution has more
    2.  in its tails than the Normal distribution.  You do not need to know the
    3.  standard deviation to use the Student-t distribution.  Graphs of the Normal distribution and the Student-t distribution look very similar.  However, the exact shape of the Student-t distribution depends on the
  • .  As the number of degrees of freedom increases the Student-t distribution becomes more and more like the Normal distribution.

QUESTION 10

  1. If you have a binomial distribution you are dealing with a proportion problem. 
     True
     False

QUESTION 11

  1. What is the proportion of international students in the following data?

Student

Undergraduate GPA

International

A

3.3

No

B

2.9

No

C

3.0

No

D

3.1

Yes

E

2.7

Yes

F

2.6

No

G

4.0

No

H

3.8

Yes

I

2.8

Yes

J

3.6

No

 

 

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