In: Statistics and Probability
The Conch Café, located in Gulf Shores, Alabama, features casual lunches with a great view of the Gulf of Mexico. To accommodate the increase in business during the summer vacation season, Fuzzy Conch, the owner, hires a large number of servers as seasonal help. When he interviews a prospective server, he would like to provide data on the amount a server can earn in tips. He believes that the amount of the bill and the number of diners are both related to the amount of the tip. He gathered the following sample information.
Customer | Amount of Tip | Amount of Bill | Number of Diners | Customer | Amount of Tip | Amount of Bill | Number of Diners | |||||||||
1 | $ | 7.70 | $ | 46.02 | 1 | 16 | $ | 3.30 | $ | 23.59 | 2 | |||||
2 | 4.50 | 28.23 | 4 | 17 | 3.50 | 22.30 | 2 | |||||||||
3 | 1.00 | 10.65 | 1 | 18 | 3.25 | 32.00 | 2 | |||||||||
4 | 2.40 | 19.82 | 3 | 19 | 5.40 | 50.02 | 4 | |||||||||
5 | 5.00 | 28.62 | 3 | 20 | 2.25 | 17.60 | 3 | |||||||||
6 | 4.25 | 24.83 | 2 | 21 | 3.90 | 58.18 | 1 | |||||||||
7 | .50 | 6.25 | 1 | 22 | 3.00 | 20.27 | 2 | |||||||||
8 | 6.00 | 49.20 | 4 | 23 | 1.25 | 19.53 | 2 | |||||||||
9 | 5.00 | 43.26 | 3 | 24 | 3.25 | 27.03 | 3 | |||||||||
10 | 6.65 | 36.01 | 2 | 25 | 3.00 | 21.28 | 2 | |||||||||
11 | 5.75 | 62.39 | 4 | 26 | 6.25 | 43.38 | 4 | |||||||||
12 | 6.00 | 34.99 | 3 | 27 | 5.60 | 28.12 | 4 | |||||||||
13 | 4.00 | 33.91 | 4 | 28 | 2.50 | 26.25 | 2 | |||||||||
14 | 3.35 | 23.06 | 2 | 29 | 3.65 | 60.26 | 5 | |||||||||
15 | .75 | 4.65 | 1 | 30 | 9.20 | 64.13 | 6 |
c-1. Conduct an individual test on each of the variables. What is the decision rule at the 0.05 level of significance? (Negative amounts should be indicated by a minus sign. Round your answers to 3 decimal places.)
C-1.
Where, n=sample size
r= Pearson correlation
The p-value for the test to test the correlation between the amount of the bill and the amount of the tip is 0.000 and less than 0.05 level of significance. Also, the sign of the correlation value is positive. Hence, the correlation between the amount of the bill and the amount of the tip has a positive significant relationship at the 0.05 level of significance.
The p-value for the test to test the correlation between the number of diners and the amount of the tip is 0.001 and less than 0.05 level of significance. Also, the sign of the correlation value is positive. Hence, the correlation between the number of diners and the amount of the tip has a positive significant relationship at the 0.05 level of significance.