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.

Note: Since you have posted a question with multiple sub parts, we will provide the solution only…

Answered: Consider the following data set, where…

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).

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.3: Measures Of Spread

Problem 1GP

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Question

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.

d) Make a statistical decision and write a conclusion statement; be sure the conclusion contains descriptive data and inferential test results.

Definition Definition Relationship between two independent variables. A correlation tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.

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