Question

The table shows the number of years of education of parent and the number of years of education of their child. Determine the correlation coefficient and briefly describe the relationship between the two variables, Conduct a hypothesis test to determine if there is a significant linear correlation between the two variables. What is the critical value, Conduct a hypothesis test to determine if there is a significant linear correlation between the two variables. What is the test statistic, Conduct a hypothesis test to determine if there is a significant linear correlation between the two variables. What is the p-value?, If there is a significant linear correlation between the variables, determine the regression equation.

Years of education of parent           13          9                 7             12          12              10             11

Years of education of their child       13          11               7             16          17               9              17

2. From 1996 to 2012, 84% of non-teacher workers were employed in private schools. If a random sample of 200 teachers in the years 1996-2012 was selected, what is the probability that between 78% and 86% were public school teachers?

Multiple Choice Answer pool for questions above:

A.	0.2147
B.	y’ = -3x + 1.5
C.	2.571
D.	There is no significant correlation between the variables, therefore we should not determine the regression equation.
E.	y’ = 1.5x - 3
F.	0.0416
G.	2.72
H.	1.725
I.	0.7853
J.	0.2305
K.	r = 0 .773, looking at the graph and the correlation coefficient, there appears to be no correlation.
L.	2.447
M.	2.015
N.	0.7695
O.	r = 0 .773, looking at the graph and the correlation coefficient, it appears to be positive linear.
P.	y’ = 0.398x + 5.45

Answer 1

Q 1)

a) Correlation coefficient :

Answer: r = 0 .773, looking at the graph and the correlation coefficient, it appears to be positive linear.

b) Hypothesis Testing :

Degrees of freedom : n-2 = 5

Answer: The critical value of t at 5% significance level is 2.571

c)

Under H0, the test statistic is

Answer: The test statistic is 2.72

d) Answer: The P value is 0.0416

e) Since the p value is less than significance level, Reject H0. Hence there is linear relationship exists between X and Y

f) Regression equation :

Answer: The regression equation is y’ = 1.5x - 3