Statistic Case Study for Bottle Company

The case ascertain that is being investigated is for a bottling company producing less(prenominal) soda than what is announce. Customers have complained that the sodas in the bottles contain less than the advertised sixteen ounces. The employees at the company have measured the amount of soda contained in each bottle. there ar thirty bottles that have been pulled from the shelves. The manager of the company would like to have a detailed score on the possible causes, if any, for the shortage in the amount of soda or if the claim is non back up explain how to mitigate the issue in the future.In order to statistically find a cause in the shortage a shot testing is conducted by finding the mingy, median, and standard aside for ounces in the bottles. Constructing a 95 percent interval will establish the mean of the population since the mean of the population is not known. There are thirty soda bottles being pulled for investigation. The mean will be calculated by averaging the a mount of ounces in each bottle and dividing the add up by the number of bottles.The data below shows the ounces in each of the thirty bottles that were pulled. The mean among the sample bottles is 14. 87. The calculation to find the mean is to add all the ounces per bottle. The keep down is 446. 1 divided by the random sample of 30. The average ounces in the bottles are less than 16 ounces. The median for the soda bottles is 14. 8. The median is imputed by dividing the random number of 30 by 2 which equals 15. practise the ounces from smallest to largest, and select the number that falls on 15.This will provide the median for the thirty bottles. The standard deviation for the ounces in the bottles is 0. 55. The standard deviation must be known in order to solve the impudence interval. To find the standard deviation, calculate the individual ounces minus the mean of the ounces and square the total (X-M)2. After the total is calculated, divide by the random count 30 minus 1 (n-1) . In order to compute the trustfulness interval of 95 percent the mean, standard deviation, and identifying the value must calculated.A confidence interval gives an estimated roll up of values which is likely to include an unknown population parameter, the estimated range being calculated from a abandoned set of sample data (Easton & McColl, n. d. ). The confidence interval of 95 percent can be plunge utilise a normal distribution calculator. The Z distribution is used in this case case because there are thirty bottles. The Z value is greater than or equal to thirty in spite of appearance the sample size. The Z value of 95 percent is 1. 96. This represents the area on the normal distribution graph between the cutoff points.The cutoff points on the chart are between -1. 96 and 1. 96. The lower and amphetamine limit will be given to locate the interval using the standard normal confidence interval. Calculate to find the interval by imputing Z. 025 equals 1. 96 stores the answer , in this case, using the Aleks calculator. Enter the mean 14. 87 +/- 1. 96 times 0. 55 divided by square root of 30. The lower limit is 14. 67 and the upper limit is 15. 07. This interval proves the soda in the bottles did not contain sixteen ounces.In Easton and McColl (n.d) article summarized riding horse up and testing hypothesis is an essential part of statistical inference. In order to formulate much(prenominal) a test, usually some theory has been put forward, either because it is believed to be true or because it is to be used as a basis for rivalry, but has not been proved. To verify the claim that the bottles contain less than sixteen ounces of soda a hypothesis test will be performed. To find the null hypothesis that represents the claim to be true or to be used as a basis of argument until it is proven. The null hypothesis is H0 greater than or equal to sixteen ounces.The alternating(a) hypothesis is H1 less than sixteen ounces. The type of test used is one tailed te sting. If using a significance take aim of . 05, a one-tailed test allots the entire alpha to testing the statistical significance in the one direction of interest. This essence that . 05 is in one tail of the distribution test statistic. When using a one-tailed test, it is testing for the possibility of the consanguinity in one direction and completely disregarding the possibility of a relationship in the former(a) direction (UCLA Statistical Consulting Group, 2007).The value of the test is calculated by the mean 1 minus mean 2. Therefore, 14. 87 16 equals -1. 13 divided by standard deviation 0. 55 divided by square root of random sample 30 equals . 375. The P value is calculated by using the formula P (Z equal to . 375). The P value is 0. 646. The P value is greater than the significance level of test which is . 05. The answer is the mean of 0. 5 0. 646. The conclusion of the test for the null hypothesis is not rejected. This suggests the alternative hypothesis must be true that the soda in the bottles is less than sixteen ounces.The type of misplay used in the hypothesis is type I error. There are several causes determining the argue for fewer ounces in the bottles. The air in the lines could prevent the soda from filling bottles, machine may acquire to be reset to fill 16 ounces to the exact measure, or machine may not be calibrated properly. Issuing a daily calibration of the machinery is a way to avoid the deficit in the future. Statistically the issue could stem from the unknown population of how many customers complained. There could possibly be a million sodas produced with only ten customer complaints.Therefore, pulling more bottles from the shelves and testing the ounces could show a diametrical alternative hypothesis and may prevent a deficit in the future. Other speculations that determine sodas from not being filled to the assoil are to keep the soda from overfilling so it is not filled to the top line. It has to have a bit of air in t he bottle so there can be room for the liquid. Less soda is in the bottles to expand if it gets heated otherwise the bottle could break. In conclusion, the customers are correct there is less than 16 ounces of soda in the bottle.