Part 2:
Mr Sweet provided Daniella with some data on his bakery shop. MyCakes also produces chocolate cakes, and this data is recorded week by week. Mr Sweet said: ‘In the last year we worked hard on a promotional campaign to retain loyal customers by offering them vouchers with discounts. This both increased the sales and evened them out: check our numbers!’ Daniella is not sure how to do that, so she asks you to review the data on her behalf.
Using the data below Choco cake sales, calculate the weekly average chocolate cake sales for years 2022 and 2023?
Year week number of cakes sold
2022 1 111
2022 2 137
2022 3 143
2022 4 124
2022 5 81
2022 6 56
2022 7 105
2022 8 82
2022 9 105
2022 10 96
2022 11 95
2022 12 75
2022 13 94
2022 14 119
2022 15 74
2022 16 116
2022 17 115
2022 18 96
2022 19 118
2022 20 64
2022 21 95
2022 22 122
2022 23 108
2022 24 102
2022 25 84
2022 26 69
2022 27 99
2022 28 80
2022 29 76
2022 30 59
2022 31 63
2022 32 71
2022 33 61
2022 34 71
2022 35 112
2022 36 77
2022 37 118
2022 38 97
2022 39 106
2022 40 107
2022 41 123
2022 42 79
2022 43 75
2022 44 99
2022 45 125
2022 46 95
2022 47 146
2022 48 103
2022 49 72
2022 50 98
2022 51 131
2022 52 79
2023 1 115
2023 2 147
2023 3 155
2023 4 145
2023 5 98
2023 6 71
2023 7 106
2023 8 85
2023 9 107
2023 10 96
2023 11 95
2023 12 89
2023 13 97
2023 14 129
2023 15 95
2023 16 115
2023 17 134
2023 18 112
2023 19 131
2023 20 72
2023 21 102
2023 22 121
2023 23 110
2023 24 114
2023 25 106
2023 26 73
2023 27 117
2023 28 92
2023 29 77
2023 30 83
2023 31 87
2023 32 95
2023 33 71
2023 34 82
2023 35 125
2023 36 81
2023 37 140
2023 38 121
2023 39 126
2023 40 116
2023 41 126
2023 42 89
2023 43 92
2023 44 121
2023 45 141
2023 46 112
2023 47 150
2023 48 122
2023 49 85
2023 50 101
2023 51 135
2023 52 91
For each year, calculate the 95% and 90% confidence intervals of the weekly average sales?
Discuss the results of your analysis with respect to the level and the variability of weekly sales in 2022 and 2023. Discuss the factors that influence the width of the confidence intervals.