Question

The weights​ (in pounds) of

6

vehicles and the variability of their braking distances​ (in feet) when stopping on a dry surface are shown in the table. Can you conclude that there is a significant linear correlation between vehicle weight and variability in braking distance on a dry​ surface? Use

α=0.01.

​Weight, x	5960	5370	6500	5100	5830	4800
Variability in braking​ distance, y	1.73	1.93	1.93	1.61	1.62	1.50

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Click here to view a table of critical values for​ Student's t-distribution.

Setup the hypothesis for the test.

H0​:

ρ

▼

0

Ha​:

ρ

▼

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

−t0=nothing

and

t0=nothing.

Calculate the test statistic.

t=nothing

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

What is your​ conclusion?

There

▼

is not

is

enough evidence at the

1​%

level of significance to conclude that there

▼

is

is not

a significant linear correlation between vehicle weight and variability in braking distance on a dry surface.

Answer 1

null hypothesis: Ho:           ρ'=		0
Alternate Hypothesis: Ha: ρ≠		0

B.The critical values are -4.604 and 4.604

correlation r='Sxy/(√Sxx*Syy) =		0.636
test stat t=	r*(√(n-2)/(1-r2))=	1.646

There is not enough evidence at the 1% level of significance to conclude that there is a significant linear correlation between vehicle weight and variability in braking distance on a dry surface.