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 _________.​

Answer 1

i) Scatter plot:

ii) To find the linear correlation coefficient.

Linear correlation coefficient is calculated as,

i	X (Bill in $)	Y (Tip in $)	X^2	Y^2	X*Y
1	31.62	3.9	999.8244	15.21	123.318
2	52.2	10.4	2724.84	108.16	542.88
3	90.36	8.62	8164.93	74.3044	778.9032
4	99.42	18.13	9884.336	328.6969	1802.485
5	60.7	10.6	3684.49	112.36	643.42
6	100.52	12.95	10104.27	167.7025	1301.734
sum:	434.82	64.6	35562.69	806.4338	5192.74

Substituting the values in 'r', we get,

  

  

  

  

  

iii) T determine the null and alternative hypotheses.

iv) Test statistic is given as,

Here, n=6 and r = 0.742

  

  

v) To find p-value at level of significance 0.01

The p-value is calculated P(|t|>2.2136) = 2 * P(t>2.21336)

Therefore, p-value = 2*0.04563 = 0.09126