M&Ms Project Report - Assignment Example

The results were that 51 bags were sampled( 17 students * 3 bags each=51) and the number of candies evaluated was 2872 which were of different colors. 2. Finding out the Standard Deviation and Mean The next phase was to identify the average number of candies/ bag. The statistical average of a sample is called mean . In our case it is 2872/51 which is equal to 56.3 candies/bag. This gives an idea whether the number of candies that was fixed to be in a bag before marketing was more or less than a predecided amount.

This is an important aspect of quality check. Apart from mean the Standard Deviation which is the positive square root of mean of squared deviations of all scores from their mean was calculated. The SD thereby indicate the spread or scatter or deviations of scores around a central value(mean). It is expressed by s= square root(summation of deviations/sample size). In our case it is + 1.9234 candies which means in some bags the probability of more or less candies than the mean(56.3) is 1.9 that is either it can be 58.2 or 54.4. 3. Confidence Interval and Its Importance The confidence interval of a parameter is the range of scores within which the parameter has a given probability of lying.

This is called fiducial probability.The two scores forming the lower and upper limits are called confidence limits. The fiducial probability is called the confidence level and when expressed as a percentage gives the degree of confidence in expecting a parameter to lie the given confidence interval. It is thus an interval estimate of a parameter and is more dependable than a point estimate( like the mean). In our analysis for example if we want to evaluate the CI we can infer that the proportion of blue candies in lying between 0.

2087 and 0.2391 is 95%. It can be calculated as follows: Upper Limit= Mean + Standard Score (z) at the level of alpha * Standard Error of mean Lower Limit= Mean - Standard Score (z) at the level of alpha * Standard Error of mean. Therefore 1-alpha=0.95 or 95% fiducial probability. This means that higher the fiducial probability wider the confidence interval and greater the probability of population mean falling in that interval but the lower will be the precision of estimate for true value of population mean.

In our case study from the confidence intervals of various candies it seems that the error of 0.11(upper limit-Mean or Mean- Lower Limit) is minimal with the yellow candies so the proportion of yellow candies can be truly estimated the most if we consider the whole population of candies/bag in the M& M industries. The number of candies with a confidence limit has a error of +0.5 4. Part 4- Testing of Hypothesis and Z test. In this portion we try to find out whether the proportions of candies which are estimated are true and there exists no whatsoever any statistical difference of significance of various candies in different bags.

The minor difference what is seen is speculated to happened by chance due to sampling and there is no significant difference (null hypothesis retained). But if the difference is statistically significant it means certainly that the proportio