solution

 

. Astudy of spending by customers in restaurants examined 1413 transactions.21 Five of the variables measured were check (total check amount divided by the number of customers at the table), minutes (the amount of time spent dining), table (the size of the table), party (the number of people in the party), and SPM (spending per minute, check divided by minutes). Here is a table of the correlations for these variables:

Check Minutes$1rn$1rn Table Party

Minutes$1rn $1rn $1rn $1rn$1rn 0.251

Table$1rn $1rn $1rn  0.045$1rn   0.083

Party −$1rn $1rn    0.306$1rn 0.137    0.379 SPM 0.689 −0.397 −0.031 −0.400

(a) Perform a significance test for each of these correlations and summarize the results.

(b) Discuss the pattern in the correlations, paying particular attention to the sign, the size, and the results of the significance

test.

(c) You performed 10 significance tests in this exercise. Suppose that youwanted to do a Bonferroni correction to take into account this fact and to keep the overall false rejection rate at 5%. In that case, youwould declare a correlation to be statistically significant only if the P-value is 0.05/10 or less. Perform the significance tests using the Bonferroni correction. Summarize the results and compare them with the results you obtained in part (a).