Consider the following data set, where the same people indicated how many siblings they have (X) and how happy they are in their lives (Y) (higher numbers for Y indicate greater happiness scores). ParticipantXYzXzYzXzYA12 B47 C35 D21 E514 F37 n = 6MX = 3.00MY = 6.00 S zXzY = SX = 1.41SY = 4.65 r = Test whether there is a significant correlation between X (# siblings) and Y (happiness). a) State the hypotheses (H0 and H1). b) Find the critical value for α = .05, 2-tailed, using the table of critical values for r at the appropriate df. c) Compute the test statistic (Pearson’s r) by filling in the rest of the information in the table (i.e., zX, zY, their product zXzY, the sum of all the zXzY products, and r). Round off values to two decimal places. d) Make a statistical decision and write a conclusion statement; be sure the conclusion contains descriptive data and inferential test results.

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Answered: Consider the following data set, where…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Consider the following data set, where the same people indicated how many siblings they have (X) and how happy they are in their lives (Y) (higher numbers for Y indicate greater happiness scores).

Participant	X	Y	z_X	z_Y	z_Xz_Y
A	1	2
B	4	7
C	3	5
D	2	1
E	5	14
F	3	7
n = 6	M_X= 3.00	M_Y= 6.00			S z_Xz_Y =
	S_X= 1.41	S_Y= 4.65			r =

Test whether there is a significant correlation between X (# siblings) and Y (happiness).

a) State the hypotheses (H0 and H1).

b) Find the critical value for α = .05, 2-tailed, using the table of critical values for r at the appropriate df.

c) Compute the test statistic (Pearson’s r) by filling in the rest of the information in the table (i.e., z_X, z_Y, their product z_Xz_Y, the sum of all the z_Xz_Yproducts, and r). Round off values to two decimal places.