Statistics Assignmet 1: Bottling Company Case Study
Assignment 1: Bottling Company Case Study
In this project we were given the case of customer complaints that the bottles of the brand of soda produced in our company contained less than the advertised sixteen ounces of product. Our boss wants us to solve the problem at hand and has asked me to investigate. I have asked my employees to pull Thirty (30) bottles off the line at random from all the shifts at the bottling plant. The first step in solving this problem is to calculate the mean (x bar), the median (mu), and the standard deviation (s) of the sample. All of those calculations were easily computed in excel. The mean was computed by entering: =average, the median by: =median, and the std. dev. by: = = std dev. The corresponding values are x bar = 14.87, mu = 14.8, and s = 0.550329055. The next step in solving the problem is to construct a 95% confidence interval for the average amount of the company’s 16-ounce bottles. The confidence interval was constructed by drawing a normal distribution with c = 95%, a = 0.050, and Zc = 0.025. The Zc value was entered into the Z◘ (z box) function in the Aleks calculator that resulted in a Z score of +1.96 and -1.96. We calculate the standard error (SE) by dividing the s by the Square root of n which is the sample size. The margin of error is calculated by multiplying the z score = 1.96 by the std. dev. = 0.5503/the square root of n = 5.4772. The result is a 0.020 margin of error. The margin of error is added to and subtracted from the mean to give two numbers the lower and upper values. The lower value is 14.85 and the upper value is 14.89. So, we can say that with 95% confidence the mean of the sample is between 14.85 and 14.89. The next step in solving the equation is to complete a hypothesis test. For this test the null and alternative hypotheses must be identified. Since the claim is that the sample is less than the mean
In this project we were given the case of customer complaints that the bottles of the brand of soda produced in our company contained less than the advertised sixteen ounces of product. Our boss wants us to solve the problem at hand and has asked me to investigate. I have asked my employees to pull Thirty (30) bottles off the line at random from all the shifts at the bottling plant. The first step in solving this problem is to calculate the mean (x bar), the median (mu), and the standard deviation (s) of the sample. All of those calculations were easily computed in excel. The mean was computed by entering: =average, the median by: =median, and the std. dev. by: = = std dev. The corresponding values are x bar = 14.87, mu = 14.8, and s = 0.550329055. The next step in solving the problem is to construct a 95% confidence interval for the average amount of the company’s 16-ounce bottles. The confidence interval was constructed by drawing a normal distribution with c = 95%, a = 0.050, and Zc = 0.025. The Zc value was entered into the Z◘ (z box) function in the Aleks calculator that resulted in a Z score of +1.96 and -1.96. We calculate the standard error (SE) by dividing the s by the Square root of n which is the sample size. The margin of error is calculated by multiplying the z score = 1.96 by the std. dev. = 0.5503/the square root of n = 5.4772. The result is a 0.020 margin of error. The margin of error is added to and subtracted from the mean to give two numbers the lower and upper values. The lower value is 14.85 and the upper value is 14.89. So, we can say that with 95% confidence the mean of the sample is between 14.85 and 14.89. The next step in solving the equation is to complete a hypothesis test. For this test the null and alternative hypotheses must be identified. Since the claim is that the sample is less than the mean