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 . 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

correlation 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 not 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 = 1.000