To whom it might concern,
Our AP Statistics class made an analyzed of your caramel-filled Ghirardelli chocolate hearts. Your company advertises the chocolates with the foil weigh approximately 8 grams individually. However, some consumers may think that your advertised weight is incorrect and the company does not meet the truth in advertising laws. Our class conducted an experiment using your caramel-filled chocolate hearts as samples, we have three samples: 32 groups of five and two separate samples of 32 individual chocolates. Each sample would contain independent chocolates and no chocolate has been recorded in more than one sample.
Our first sample is distribution of the individual chocolates. Our study concludes the mean weight to be approximately 8.3136 g with standard deviation .5449 g and ranges from 7g to 9.2g. The box plot shows left skewed association and has a median at 8.4. However, the box plot has no outliers and is large enough to use the Central Limits Theorem to assume the sample chocolate hearts come from a Normal population.
Our first sample is distribution of the individual chocolates. Our study concludes the mean weight to be approximately 8.3136 g with standard deviation .5449 g and ranges from 7g to 9.2g. The box plot shows left skewed association and has a median at 8.4. However, the box plot has no outliers and is large enough to use the Central Limits Theorem to assume the sample chocolate hearts come from a Normal population.
To find the true mean weight of the chocolates, we use the 95% confidence interval equation for 1 mean test of significance of 5%.
Therefore we are 95% confidence that the true mean weight of the chocolate should be between 8.1909 grams to 8.4463 grams.
-3.232 =
-.2188= 8.3136
With foil paper, the advertised weight of the Ghirardeli chocolate heart should be 8.0948g to meet the truth in advertising laws. There should be no more than one of every thousand less than 8.0948g.
The next sample contains groups of chocolate hearts in 5. The data has a mean weight of 41.6906 grams with standard deviation of 1.1713 g, ranges from 39.2g to 45.6g. This sample is also slightly skewed to the left with two outliers, the median is at 41.5. As the sample size is also large enough to use the Central limits Theorem, we can also assume that the sample chocolate hearts come from a Normal distribution.
To find the true mean weight of five chocolate hearts’ weight, we will also use the 95% confidence interval equation for 1 mean.
The true mean weight of five chocolate hearts is between 41.2848and 42.0964.
-3.232 =
-.6693=
With foil paper, the advertised weight of the groups of five Ghirardeli chocolate heart should be 41.0213g to meet the truth in advertising laws. There should be no more than one of every thousand less than 41.0213g.
No more than one out of every thousand package of five hearts should be under 41.0213g, the advertised weight.
Thank you for your patient.
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