Question

Using the data given in the table below, answer the following questions. (Round your final answers to 3 decimal places.) Moviegoer Snack Spending (n 10 Age (X) 30 50 34. 12 37 Spent (Y) 2.85 6.50 1.50 6.35 6.20 6.75 3.60 6.10 8.35 4.35 36 26 18 46 Click here for the Excel Data File (a) Use Excel, MegaStat, or MINITAB to calculate the correlation coefficient. (A negative value should be indicated by a minus sign.) calc (b) Use Excel or Appendix D to find t025 for a two-tailed test at a- .05. t 025 (c) Calculate the t test statistic. (Negative value should be indicated by a minus sign.) calc (d) Should we reject the null hypothesis of zero correlation? No Yes

Answer 1

X	Y	XY	X²	Y²
30	2.85	85.5	900	8.1225
50	6.50	325	2500	42.25
34	1.50	51	1156	2.25
12	6.35	76.2	144	40.3225
37	6.20	229.4	1369	38.44
33	6.75	222.75	1089	45.5625
36	3.60	129.6	1296	12.96
26	6.10	158.6	676	37.21
18	8.35	150.3	324	69.7225
46	4.35	200.1	2116	18.9225
∑X=322	∑Y=52.55	∑XY=1628.45	ΣX²  =11570	∑Y2 =315.7625

r = COV(X,Y)/σ_XσY

= (1628.45/10)-(322/10)(52.55/10)/√(11570/10)-(322/10)²√(315.7625/10)-(52.55/10)²

^{= (162.845-169.211)/}√(1157-1036.84)√(31.57625-27.615025)

= -6.366/(10.961)(3.9612)

= -0.146

b)

n = 10 and  α = 0.05

Null hypothesis H₀: P=0

Alternative hypothesis H₁: p ≠ 0

  t_(α/2,n-2) =±2.30

c)

The stati stic tca-

t_cal = -0.146√10-2/√1-(-0.146)² = -0.4174

d) t_{cal = -0.4174 lies between the critical value} ±2.30

NO,do not reject the null hypothesis of linear relation