Question

Listed below are amounts of bills for dinner and the amounts of the tips that were in Construct a caterplot, find the value of the lines correlation coefficient and find the P value of Determine whether there is sufficient evidence to support claim of the correlation between the two variables. Use a significance level of 0.05. Il everyone were to tip with the same percentage, what should be the value of r? BH (dollars) 32.77 3.02 8431 8804 61.00 114.67 Tip (dollars) 3.96 16.48 9.30 11.16 12.83 Construct a wowerplot. Choose the correct graph below. ОА OB OC OD @ . D 120 120 BARON 120 120 Amour mount The linear correlation coefficientis Flound to three decimal places as needed) Determine the nul and alterative hypotheses Hop Hip (Type Integers or decimals. Do not round) The most statistics (Round to two decimal places as needed) The P-values (Round to the decimal places as needed)

Answer 1

Solution :

1) Option B)

Scatterplot of tip amount and bill amount is;

Scatterplot of Tip Amount ($) vs Bill Amount ($) 17.5 15.0 12.5 Tip Amount ($) 10.0 7.5 5.0 30 40 50 60 90 100 110 120 70 80 Bill Amount ($)

2) Correlation coefficient :

7= (X – X)(Y -Y) V(X - X)(Y - Y)2

Where = Mean of Variable X

T

  $\bar{y}$ = Mean of Variable Y

$r = \frac{428.0523}{4162.3039*85.3358}$

	Bill (X)	Tip (Y)	(X - Mean(X))	(Y - Mean(Y))	(X -Mean(X))^2	(Y - Mean(Y))^2	(X - Mean(X))(Y - Mean(Y))
	32.77	3.95	-39.0316667	-6.72	1523.471003	45.1584	262.2928
	53.02	9.77	-18.7816667	-0.9	352.7510028	0.81	16.9035
	84.31	16.48	12.5083333	5.81	156.4584028	33.7561	72.67341667
	85.04	9.83	13.2383333	-0.84	175.2534694	0.7056	-11.1202
	61	11.16	-10.8016667	0.49	116.6760028	0.2401	-5.292816667
	114.67	12.83	42.8683333	2.16	1837.694003	4.6656	92.5956
Total	430.81	64.02	0	0	4162.303883	85.3358	428.0523
Mean	71.80166667	10.67
	r	0.718231272

3) For testing of correlation coefficient :

$H_{0} : \rho = 0$

$H_{a} : \rho \neq 0$

Where $\rho$ is population correlation

The test statistic is ;

$t = \frac{r \sqrt{n-2}}{\sqrt{1-r^2}}$

where ,

r = sample correlation coefficient = 0.718

n = sample size = 6

$t = \frac{0.718\sqrt{4}}{\sqrt{1-0.5155}}$

Test statistic is t = 2.06

P Value :

In Excel : =TDIST(2.064 , 4 , 1) = 0.054

P - Value = 0.054

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 bil amount and tip amount .