MKTG 4682 Homework Assignment #1: Standard Deviation and Confidence Intervals

Instructions:Use the formulas and procedures provided in the Basic Statistics Review module to SOLVE the following business problems and ANSWER the associated questions. BE SURE TO SHOW YOUR CALCULATIONS AND WORK for EACH QUESTION to receive full credit. The homework assignment is worth 1,000 points in all Question #1 is worth 334 points, and Questions #2 and #3 are each worth 333 points. [SPRING 2023]

The following data represents the 2022 number of new customers acquired by each of Massage Envys 14 sales representatives. Use the numbers shown in the table for your calculations.

RepNew customers(x )Squared (x )²Divide total by n-1Take SQRT

Kara2750||Andy3300||Pat5200||Sam4750||Carly4350||Mandy6000||Laura3200||Gil4400||Ally5100||Wendy3000||JJ6150||Lonny5350VVFranky4200Pam3850TOTAL => all x valuesTOTAL => all squared ²n =^ VARIANCE (s²)

^

STANDARD

DEVIATION (s)

Mean (

) =

PROBLEM #1: Use the table above and the procedures learned in class to calculate the standard deviation (notated as s) of the average new customers acquired by ALL the sales reps in 2022. What is the standard deviation of average new customers per representative?

PROBLEM #2: Apply the results of your answer to Question #1 and use the table below and the procedures learned in class to calculate the 95% confidence interval for average new customers per rep in 2022. What is the 95% confidence interval (CI) for average new customers? BE SURE TO SHOW YOUR WORK for each value you calculate below. Formulas from class are provided on page 3.

Mean value (

)Stdev (s)nSE of meanz-value1.96Plus/minus valueUpper CI valueLower CI value

PROBLEM #3: Massage Envy provides an Annual New Customer Bonus to its sales reps with a SIGNIFICANTLY higher than average number of new customers at a confidence level of 95%. Based on your answers to the first two problems, WHICH REPS earnthe Annual New Customer Bonus for producing new customers MORE THAN the 95% confidence interval? Massage Envy also places reps with a SIGNIFICANTLY lower number of new customers on productivity probation. WHICH reps are placed on probation for producing LESS THAN the 95% confidence interval? BE SURE TO USE THE INPUTS IN THE QUESTIONS AND THE RESULTS OF YOUR CALCULATIONS TO CLEARLY EXPLAIN WHY OR WHY NOT.

x x x x (xx)