Problem #1
Bumble followed up with his data collection and gathered a new dataset of measures around sales at his grocery store per customer per visit, combining both observations and customer survey, listed in file:
| ID | Spending ($) | Duration (minutes) | Age | Gender (0=male, 1=female) | Travel (minutes) | Dietary Preference | Member? |
| 1 | 65 | 21 | 18 | 0 | 15 | Regular | Yes |
| 2 | 26 | 4 | 25 | 0 | 20 | Regular | No |
| 3 | 44 | 31 | 17 | 0 | 15 | Regular | No |
| 4 | 31 | 33 | 48 | 0 | 10 | Low-carb | No |
| 5 | 5 | 9 | 28 | 0 | 25 | Low-fat | Yes |
| 6 | 95 | 47 | 55 | 0 | 40 | Regular | No |
| 7 | 12 | 35 | 33 | 0 | 20 | Low-fat | Yes |
| 8 | 125 | 43 | 51 | 0 | 35 | Low-carb | No |
| 9 | 8 | 7 | 25 | 0 | 5 | Regular | Yes |
| 10 | 85 | 18 | 32 | 0 | 10 | Low-carb | No |
| 11 | 80 | 49 | 29 | 0 | 25 | Regular | No |
| 12 | 102 | 61 | 28 | 0 | 50 | Regular | No |
| 13 | 89 | 36 | 30 | 0 | 15 | Low-carb | No |
| 14 | 68 | 48 | 19 | 0 | 60 | Low-fat | No |
| 15 | 122 | 57 | 62 | 0 | 10 | Low-carb | No |
| 16 | 73 | 56 | 30 | 1 | 35 | Low-fat | Yes |
| 17 | 188 | 68 | 40 | 1 | 70 | Regular | Yes |
| 18 | 256 | 47 | 51 | 1 | 25 | Low-carb | No |
| 19 | 113 | 53 | 45 | 1 | 30 | Low-fat | Yes |
| 20 | 88 | 39 | 68 | 1 | 5 | Low-fat | Yes |
| 21 | 188 | 57 | 29 | 1 | 10 | Low-carb | Yes |
| 22 | 76 | 27 | 30 | 1 | 30 | Low-fat | No |
| 23 | 197 | 67 | 47 | 1 | 45 | Low-carb | Yes |
| 24 | 99 | 30 | 33 | 1 | 20 | Regular | Yes |
| 25 | 238 | 61 | 90 | 1 | 15 | Low-carb | No |
| 26 | 47 | 52 | 16 | 1 | 30 | Low-fat | Yes |
| 27 | 166 | 26 | 43 | 1 | 40 | Low-carb | Yes |
| 28 | 85 | 51 | 36 | 1 | 60 | Low-fat | Yes |
| 29 | 159 | 64 | 71 | 1 | 45 | Regular | Yes |
| 30 | 200 | 50 | 48 | 1 | 20 | Low-fat | No |
| Regular | Low-fat | Low-carb |
| 65 | 5 | 31 |
| 26 | 12 | 125 |
| 44 | 68 | 85 |
| 95 | 73 | 89 |
| 8 | 113 | 122 |
| 80 | 88 | 256 |
| 102 | 76 | 188 |
| 188 | 47 | 197 |
| 99 | 85 | 238 |
| 159 | 200 | 166 |
The variables are spending (US $), duration of shopping (minutes), age (years) gender (0 = male, 1 = female), travel time to store (minutes), dietary preference (regular, low-fat, or low-carb), and store membership (yes/no) for each of the 30 customers that he sampled and tracked.
First, he wants to understand the population (true) average amount of spending ($) per customer per visit for all his customers.
1-1 What is his point estimation of the population mean spending? (select from the dropdown)
$ [ Select ] ["67.70", "85.00", "88.50", "100.83", "104.33"]
1-2 Construct a 95% confidence interval for the population mean spending. (select from the dropdown)
Lower limit = $ [ Select ] ["24.37", "25.28", "76.46", "79.05", "125.20", "129.62"]
Upper limit = $ [ Select ] ["24.37", "25.28", "76.46", "79.05", "125.20", "129.62"]
1-3 What is the most appropriate interpretation of the above 95% confidence interval? (select from the dropdown)
[ Select ] ["The population mean spending value is captured in the two limits without fail.", "95% of all his customers spend amounts between the two limits.", "With 95% certainty, the population mean spending value is captured in the two limits.", "With 95% certainty, all his customers spend amounts between the two limits."]