Question

A researcher suspects that there is a relationship between an individual’s level of impulsiveness is inversely related to their memory. To test this hypothesis, she administers scale measuring impulsiveness and a free recall test, to a group of 12 volunteers. The impulsiveness scale yields a score ranging from 1 to 10, where higher scores indicate greater amounts of impulsiveness. The free recall test is scored in terms of the number of items correctly recalled from a 20 item list The resulting scores are as follows:

Participant                 Impulsiveness Score             Free Recall

1                                   9                                            7

2                                  10                                            5

3                                  8                                            10

                          4                                  3                                          18

5                                    5                                            15

6                                  7                                          11

7                                    8                                            9

8                                   6                                            12

9                                    1                                          18

10                                    2                                          17

a) Draw a scatter diagram for these data (5 points.)

b) How strong is the relationship between impulsiveness and recall? Calculate the correlation coefficient for these data (15 points.)

c) Interpret the correlation coefficient, What does the value of the correlation coefficient tell us about the relationship between impulsiveness and memory?

2. An imaginative anthropologist has been measuring the heights of hobbits and has found the following data :

m = 44 inches             s = 6 inches

Assume that the heights of hobbits are normally distributed and answer the following questions below (5 points each):

a) What proportion of the hobbit population taller than 45 inches

b) What proportion of hobbits have heights between 35 and 38 inches?

c) What percentage of the population is shorter than 46 inches?

d) What heights make up the most extreme 7% (both extremely tall and short, but a total of 7% of the population) of the hobbit.population?

e) What heights make up the middle 90% of the hobbit population?

3. Given a distribution with a mean of 50 and a standard deviation of 6, convert the following raw scores to the standard scores indicated: (5 pts.)

a) X=53 to a GRE score

b) X= 36 to an IQ score

4) An urn contains the following distribution of marbles:

Color of marble         f

blue                15

green              12

red                  13

yellow            17

purple              18

a) What is the probability of selecting a yellow marble at random?

b) What is the probability of selecting a green, a purple or a red marble at

random?

c) What is the probability of selecting, with replacement, 3 marbles, one red, one

yellow and one purple

d) What is the probability of selecting two blue marbles, in a row, with

replacement?

e) What is the probability of selecting two blue marbles in a row without replacement? (10 points)

4. Use the normal curve to answer these questions about the probabilities of heights in the hobbit population, discussed in question 2.

a) What is the probability of randomly selecting a hobbit who is either shorter than 40 inches or taller than 50 inches?

b) What is the probability of randomly selecting two hobbits from the population that are taller than 50 inches?

Answer 1

X = heights of hobbit Xa Normal (44, 6). (a, P (X345) = P(Z > 45-44) = P(23 0.167) = 0.434 -> 434 out of lovo have height = 45 b. P (35 <x<38) - P(35-44 <Zc38-44) = P(-1.5<2 <-1) = P( ZC-1) - P(Z <-1.5) = 0.16 - 6.07 = 0.09. - 9 out of 100 have height b/w 35 and 32 ic P(X<46) = P/2246-44) = P(2<0.33) = 0.63 2) 63% have height 96

We want x, and xr , such that P(x Cn.) + P(xsu) = 7%. 2 Now, P(alt) = 3.5% - Plat = 0.035 Equ (1 can be P(2x - 44 ) + P(252, 44 ) -5.63 So, x, -44 - - 1.81 2 x = 83.14 6 x = 54.86 Thank you. Please Doop a like Note: We are legally bounded to Solve only 4 parts of the question, which has been done