Nabisco Hundred Calorie Packs Lorna Doone Short Bread Cookies Laurie Doyle, Beth Connolly, Helen Kushnir
Nabisco History • 1898 New York Biscuit Company by Adolphus Green and William Moore • 1906 moved headquarters from Chicago to New York • Lorna Doone Short Bread Cookies first introduced in 1912
Nabisco History • End of 1960’s leading cookie and cracker manufacturer • 1971 named Nabisco • 100 calorie packs now a $100 million brand • Over 30 different varieties
Purpose • We are testing to see if each of the individual bags weigh the standard weight of 21 grams, as marked on the packages. • We are also testing to see if the amount of cookies present in each bag is the same, and that certain bags don’t have more cookies than another. • Making sure the consumer gets their money’s worth! • We also want to make sure the weight isn’t over the expected amount so that there really is 100 calories in each bag
Procedure • Went to 7 different stores and purchased a box from each store which allowed for a varied sample size • The 7 stores were Acme, Genuardi’s, Giant, Rite Aid, Wegmans, Target, and Shop Rite • We randomly picked out a box from each store to purchase • Allowed the samples to be more randomized • Each box has 6 packages of cookies which allowed of a total sample size of 42 packages • Counted and weighed the cookies from each of the 42 packages individually and recorded the results • Put the sample size together to compare our calculated weight with the expected weight of 21 g per package • Used the cookie counts to calculate a 95% confidence interval for the number of cookies per package
Statistics for Grams Min: 20.04 Q1: 21.53 Med: 21.965 Q3: 22.25 Max: 24.06
20.04 21.53 21.965 22.25 24.06 Box PlotGrams per package Weight in Grams
One Sample t-Test Assumptions • SRS • Normal Population or 1. 2.
grams 7.3909 grams We reject Ho in favor of Ha because the p-value We have sufficient evidence that the average amount of grams in one package of shortbread 100 calorie cookies is greater than 21 grams.
One Sample t-Confidence Interval ( 21.651, 22.14 ) We are 95% confident that the average number of grams per package is between 21.651 and 22.14 grams. We reject Ho in favor of Ha because the expected mean of 21 grams does not fall within the 95% confidence interval. We have sufficient evidence that the average number of grams in a package is greater than 21 grams.
Finding expected number of cookies per package We took and SRS of five individual shortbread cookies and weighed them. The average weight of one cookie was 1.04. We used the expected number of grams per package and divided it by the average weight of a cookie to get the expected number of cookies per package. 20.19 cookies is the expected value per package.
Statistics for Cookies Min:18.25 Q1: 19 Med:20 Q3:20.5 Max:22
Box PlotCookies per package 18.25 19 20 20.5 22 Number of Cookies
One Sample t-Test Assumptions 1. 2. • SRS • 2. Normal Population or
One Sample t-Test cookies -1.8994 cookies We reject Ho in favor of Ha because the p-value .0323 > . We have sufficient evidence that the mean number of cookies in a bag is less than 20.19.
One Sample t-Confidence Interval ( 19.687 , 20.205 ) We are 95% confident that the average number of grams per package is between 19.687 and 20.205 cookies. We fail to reject Ho in favor of Ha because the expected mean of 20.19 cookies falls within the 95% confidence interval. We have sufficient evidence that the average number of cookies in a package is equal to 20.19 cookies.
63.69% of the change in number of cookies per package is determined by the change in weight. For ever increase by one cookie, the weight increases by .7539 cookies.
Application • The 100 calorie packs are often used in diets so is important that each package truly has the amount of cookies it tell people it does • All of us eat the 100 calories cookies and were interested in seeing how varied in weight and count the packages really are • It allows us to test how true the company’s claim is of 21 grams of cookies per package • Shows us if we’re really getting our money’s worth or getting ripped off
Bias/Sources of Error • The broken cookies in some of the packages • Even though each individual package was weighed on the same scales, two different scales were used throughout the whole experiment • Had to estimate ourselves the average number of expected cookies per package
Conclusions/Opinions • We conclude that the 100 calorie packs are not 100 calories because the actual average weight in grams is higher that the expected weight in grams. • We also conclude that the customer gets their money’s worth and the number of cookies in each bag is relatively the same • We were very surprised to find that the average weight in grams was higher than the expected weight.