Homework 2  - Due 6/20.  Turn in your work on a separate piece of paper. SHOW WORK OR INTERMEDIATE CALCUALTIONS FOR FULL CREDIT.

 

The following data consists of paired scores from students measuring their self-reported statistics anxiety and their final grade in a statistics class (note: this is a sample of data from the first homework).

 

Anxiety

Grade

 

2

88

 

6

84

 

11

77

 

9

85

 

5

92

 

7

89

 

10

74

 

9

92

mean

7.38

85.13

sd

2.97

6.64

 

Part I: Correlation and Regression

  1. Compute the correlation between anxiety and final grade.
  2. Provide a interpretation for this correlation. What does it tell you about the relationship between anxiety and grades?
  3. What is the probability of obtaining a correlation of this magnitude assuming that the true population correlation is zero (D = 0)? (You can use > < to describe the probability).
  4. Derive and show the prediction equation for predicting final grade from statistics anxiety for this data.
  5. State in words what the slope value for this data means.
  6. Predict the final grade for a student with an anxiety score of 3.
  7. Use the first 5 scores in the table ONLY  to compute the standard error of the estimate.
  8. Assuming homoscedasticity, for all individuals in the population with an anxiety score of 3, what percent are expected to have actual final grades of 80 or less ?

 

Part II. – Probability

  1. (Use enumeration) You are going to toss a coin 3 times. What is the probability that
    1. You will get exactly one head?

 

    1. You will get AT LEAST one head?

 

    1. The probability that you will get NO heads?

 

  1. You have a die and a deck of cards. You roll the die and chose a card. What is the probability that you will get either a 4 or a queen?

 

  1. You have two dice and a deck of cards. You are going to roll both dice together, and then chose a card from the deck. What is the probability that the sum of your dice will be greater than 9, and that your card will be a face card?

 

  1. In a normally distributed population with : = 45 and F=3.5, what is the probability of randomly choosing a member with x = 39.5 or greater?