t-Distribution. Source: Pearson t-Distribution. Source: Pearson Braking Distance
ID: 3201633 • Letter: T
Question
t-Distribution. Source: Pearson t-Distribution. Source: Pearson Braking Distances: Wet Surface The weights (in pounds) of eight vehicles and the variabilities of their braking distances (in feet) when stopping on a wet surface are shown in the table. At = 0.05, is there enough evidence to conclude that there is a significant linear correlation between vehicle weight and variability in braking distance on a wet surface?
Weight, x 5890 5340 6500 4800 5940 5600 5100 5850
Variability, y 2.92 2.40 4.09 1.72 2.88 2.53 2.32 2.78
a)State the null and the alternative hypotheses.
b) Determine the critical values.
c) Find the standardized test statistic.
d) Make a decision and interpret your decision in the context of the original claim.
Question 1
State Ho and Ha.
Ho: 0
Ha: < 0
Ho: 0
Ha: > 0
Ho: = 0
Ha: 0
Find the critical value(s). (round your answer to 3 decimals)
to= ± _______
Find the standardized test statistic. (round to 3 decimal places)
t =______
Determine whether to reject or fail to reject the Ho and interpret your decision.
Reject Ho. There is not sufficient evidence at the 5% level of significance to conclude that there is significant correlation between vehicle weight and variability in braking distance on a wet surface.
Reject Ho. There is enough evidence at the 5% level of significance to conclude that there is significant linear correlation between vehicle weight and variability in braking distance on a wet surface.
Fail to reject Ho. There is enough evidence at the 5% level of significance to conclude that there is significant linear correlation between vehicle weight and variability in braking distance on a wet surface.
Fail to reject Ho. There is not sufficient evidence at the 5% level of significance to conclude that there is significant correlation between vehicle weight and variability in braking distance on a wet surface.
Ho: 0
Ha: < 0
Ho: 0
Ha: > 0
Ho: = 0
Ha: 0
Find the critical value(s). (round your answer to 3 decimals)
to= ± _______
Find the standardized test statistic. (round to 3 decimal places)
t =______
Determine whether to reject or fail to reject the Ho and interpret your decision.
Reject Ho. There is not sufficient evidence at the 5% level of significance to conclude that there is significant correlation between vehicle weight and variability in braking distance on a wet surface.
Reject Ho. There is enough evidence at the 5% level of significance to conclude that there is significant linear correlation between vehicle weight and variability in braking distance on a wet surface.
Fail to reject Ho. There is enough evidence at the 5% level of significance to conclude that there is significant linear correlation between vehicle weight and variability in braking distance on a wet surface.
Fail to reject Ho. There is not sufficient evidence at the 5% level of significance to conclude that there is significant correlation between vehicle weight and variability in braking distance on a wet surface.
Explanation / Answer
r( X,Y) =Co V ( X,Y) / S.D (X) * S.D (y)
r( X,Y) = Sum(XY) / N- Mean of (X) * Mean of (Y) / Sqrt( X^2/n - ( Mean of X)^2 ) Sqrt( Y^2/n - ( Mean of Y)^2 )
Co v ( X, Y ) = 1 /8 (124226) - [ 1/8 *45020 ] [ 1/8 *21.64] = 305.862
S. D ( X ) = Sqrt( 1/8*255373800-(1/8*45020)^2) = 502.96
S .D (Y) = Sqrt( 1/8*61.779-(1/8*21.64)^2) = 0.637
r(x,y) = 305.862 / 502.96*0.637 = 0.9547
If r = 0.9547> 0 ,Perfect Positive Correlation
Given that,
value of r =0.9547
number (n)=8
null, Ho: =0
alternate, H1: !=0
level of significance, = 0.05
from standard normal table, two tailed t /2 =2.447
since our test is two-tailed
reject Ho, if to < -2.447 OR if to > 2.447
we use test statistic (t) = r / sqrt(1-r^2/(n-2))
to=0.9547/(sqrt( ( 1-0.9547^2 )/(8-2) )
to =7.86
|to | =7.86
critical value
the value of |t | at los 0.05% is 2.447
we got |to| =7.86 & | t | =2.447
make decision
hence value of | to | > | t | and here we reject Ho
ANSWERS
---------------
null, Ho: =0
alternate, H1: !=0
test statistic: 7.86
critical value: -2.447 , 2.447
decision: reject Ho. rhere is enough evidence at the 5% level of significance
to conclude that there is significant linear correlation between vehicle weight and
variability in braking distance on a wet surface.
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