Question

Listed below are amounts of bills for dinner and the amounts of the tips that were left. Construct a​ scatterplot, find the value of the linear correlation coefficient​ r, and find the​ P-value of r. Determine whether there is sufficient evidence to support a claim of linear correlation between the two variables. Use a significance level of α = 0.01. If everyone were to tip with the same​ percentage, what should be the value of​ r?

Bill​ (dollars)    31.62 52.20    90.36 99.42    60.70    100.52
Tip​ (dollars)    3.90    10.40    8.62 18.13 10.60    12.95

Construct a scatterplot.

The linear correlation coefficient r is __​______.

(Round to three decimal places as​ needed.)

determine the null and alternative hypotheses.

Ho​: ρ(1)____________ ________________
H1​: ρ(2)___________    ________________

(Type integers or decimals. Do not​ round.)

The test statistic is _________. ​

(Round to two decimal places as​ needed.)

The​ P-value is _________.​

(Round to three decimal places as​ needed.)

Because the​ P-value of the linear correlation coefficient is (3) ___________the significance​ level, there (4)____________ sufficient evidence to support the claim that there is a linear correlation between bill amounts and tip amounts.

If everyone were to tip with the same​ percentage, then r = ________ .
​(Round to three decimal places as​ needed.)

(1) ≠
>
=
   <
(2) >
   =
≠
<
(3) greater than
   less than or equal to
(4) is not
   is

Answer 1

linear correlation coefficient r='Sxy/(√Sxx*Syy) =

0.763

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

test stat t=	r*(√(n-2)/(1-r2))=	2.36
P value    =	0.078	(from excel:tdist(2.3578,4,2)

Because the​ P-value of the linear correlation coefficient is greater than the significance​ level, there is sufficient evidence to support the claim that there is a linear correlation between bill amounts and tip amounts.

v If everyone were to tip with the same​ percentage, then r = 1.000