Question

A student wonders if the number of hours a student studies for an test is related to the score the student gets on the test. She surveyed her classmates and made these observations. The number of hours of study (x) 6,8, 10, 12, 15 The score obtained out of 100 (y) 70, 76,68 80, 95 (a) Find the correlation r between the number of hours of study and the score obtained. (b) Find the critical values for r (c) Determine if there is significant linear correlation in the population. (d) Clearly state the conclusion.

Answer 1

a)

	x	y	xy	x2	y2
	6	70	420	36	4900
	8	76	608	64	5776
	10	68	680	100	4624
	12	80	960	144	6400
	15	95	1425	225	9025
Total	51	389	4093	569	30725

The formula for correlation correlation is,

So,

The correlation r between the number of hours of study and the score obtained is 0.8349

b)

Degrees of freedom = n - 2 = 5 -2 = 3

α = 0.05 (two-tails)

From the Pearson correlation table, the critical value for α = 0.05 (two-tails) and df =3  is 0.878

i.e df = 3

r-critical = 0.878

c)

Decision rule:

If the computed r value is greater than the r tabular value, reject H0.

In our problem,

Computed value of r = 0.8349

Tabulated value of r (r- critical) = 0.878

Since the computed value of r is less than r-critical, there is no enough evidence to reject H0.

So, we fail to reject H0.

It is conclude that there is no significant linear correlation in the population.