A cereal company wants to see which of two promotional strategies, supplying coupons in a local newspaper or including coupons in the cereal package itself, is more effective. (In the latter case, there is a label on the package indicating the presence of the coupon inside.) The company randomly chooses 80 stores around the country?all of approximately the same size and overall sales volume?and promotes its cereal one way at 40 of these sites, and the other way at the other 40 sites. (All are at different geographical locations, so local newspaper ads for one of the sites should not affect sales at any other site.) Unfortunately, as in many business experiments, there is a factor beyond the company's control, namely, whether its main competitor at any particular site happens to be running a promotion of its own.

The file Cereal Example.xlsx has 80 observations on three variables:

? Sales: number of boxes sold during the first week of the company's promotion

? Promotion Type:1 if coupons are in local paper, 0 if coupons are inside box

? Competitor Promotion:1 if main competitor is running a promotion, 0 otherwise

Carry out appropriate analyses on the data to address the objective in question. Motivate why you are doing the specific one or more analyses and interpret the results statistically as well within the framework/context of the given problem. You need to make clear what your assumptions are along with any relevant justifications from data, adequacy or limitation of the data and how reliable your findings are. Avoid speculating much on other data variables that should have been there. Assume that you don't need to worry about any new variables as such, but comment on whether there is a better sampling design for the future.

Question 2 (25 Marks)

Carry out an analysis based on simulations that gives an insight into what kind of sample size would be adequate to assume CLT for sample mean based on an i.i.d sample from

(a) Bernoulli distribution

(b) Exponential distribution

It is

Carry out an analysis based on simulations that gives an insight into what kind of sample size would be adequate to assume CLT for sample mean based on an i.i.d sample from

(a) Bernoulli distribution

(b) Exponential distribution

It is up to your creativity on on how you define adequacy. Insight means helping someone understand how the requisite sample size changes for different values of the parameters. It will also be interesting if you can demonstrate when you are testing some hypothesis, how much a CLT assumption is going to impact the type I and type II errors.

Sales for Promotion Type 1 169 242 175 253 236 158 231 205 169 178 200 200 229 230 193 234 218 211 218 152 223 174 225 194 197 223 150 190 196 202 197 220 245 196 222 202 289 229 193 216 Sales for Promotion Type 2 160 209 175 172 206 188 185 171 175 207 209 207 181 222 197 166 189 178 167 210 228 241 167 189 191 224 151 220 202 220 184 205 216 201 208 187 197 197 195 200 Sales for Promotion Type 1 Mean Standard Deviation Combined/Pooled Standard Deviation Standard Error T-Statistics P-Value 207.1 28.9480525008116 25.05030196 5.601417804 2.173556843 0.032733387 Sales for Promotion Type 2 Function Used 194.925 20.4216922124615 AVERAGE() STDEV.S() Underoot (S1^2 + S2^2)/2 Difference of means / Standard Error t.dist(t,79,2) Store 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 Sales Promotion Type 169 1 242 1 175 1 253 1 236 1 158 1 231 1 205 1 169 1 178 1 200 1 200 1 229 1 230 1 193 1 234 1 218 1 211 1 218 1 152 1 223 1 174 1 225 1 194 1 197 1 223 1 150 1 190 1 196 1 202 1 197 1 220 1 245 1 196 1 222 1 202 1 289 1 229 1 193 1 216 1 160 0 209 0 175 0 172 0 206 0 188 0 185 0 Competitor Promotion 1 0 1 0 0 1 0 1 1 1 0 1 0 0 1 0 0 0 0 1 0 1 0 1 1 0 1 1 0 1 1 0 0 1 0 1 0 0 1 0 1 0 0 1 0 0 1 Thisisis fictitious fictitiousdata. data. This 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 171 175 207 209 207 181 222 197 166 189 178 167 210 228 241 167 189 191 224 151 220 202 220 184 205 216 201 208 187 197 197 195 200 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 1 0 1 1 1 0 1 0 0 0 1 1 1 0 1 1 0 0 0 0 1 1 0 0 0 0 0 0 ctitious data. titious data