Question

# The number of hours 10 students spent studying for a test and their scores on that...

The number of hours 10 students spent studying for a test and their scores on that test are shown in the table. Is there enough evidence to conclude that there is a significant linear correlation between the​ data? Use alphaequals0.05.

Hours, x   Test score, y
0   40
1   40
2   55
4   49
4   65
5   67
5   73
6   70
7   81
8   93

Setup the hypothesis for the test.

Upper H 0H0​:

rhoρ

less than or equals≤

less than<

equals=

greater than>

greater than or equals≥

not equals≠

0

Upper H Subscript aHa​:

rhoρ

less than or equals≤

less than<

equals=

greater than>

greater than or equals≥

not equals≠

0

Identify the critical​ value(s). Select the correct choice below and fill in any answer boxes within your choice.

​(Round to three decimal places as​ needed.)

A.The critical value is

nothing.

B.The critical values are

minus−t 0t0equals=nothing

and

t 0t0equals=nothing.

Calculate the test statistic.

tequals=nothing

​(Round to three decimal places as​ needed.)

What is your​ conclusion?

There

is not

is

enough evidence at the

55​%

level of significance to conclude that there

is

is not

a significant linear correlation between hours spent studying and test score.

Let denotes the true correlation coefficient between hours and test score.

To test against

Here

sample correlation coefficient

and sample size

The test statistic can be written as

which under H0 follows a t distribution with n-2 df.

We reject H0 at 5% significance level if

Now,

The value of the test statistic =

and critical value

Since , so we reject H0 at 5% significance level.

There is enough evidence at the 5​% level of significance to conclude that there is a significant linear correlation between hours spent studying and test score.