1. The mean of the bottling Company Case Study is 475.62(sum of all ounces of the bottles that were randomly selected on all three shifts)/30(amount of bottles that were randomly selected on all three shifts)=15.85(mean/average of ounces).
When evaluating the median of an even data set the two middle numbers are added together and the mean of those two numbers is taken. In this case, the median of the Bottling company case study is 15.98 + 16.00 = 31.98/2 = 15.49. the median is 15.49.
The standard deviation is calculated as
σ = √[ ∑(x-mean)^2 / N ]
σ = √13.115/29 = √.4522 = 0.6724581771381771
2.
N=30, x = 15.85, s= .067, and z-1.96
CI = 1.96 + or – (.67/the square root of 30 or 5.47) = 15.85 + or minus .24,. the
Answer is 15.585 + .24 = 16.09, 15.85-.24 = 15.61,
95% Confidence intervals are (15.61, 16.09)
3.
(H0) Alternate hypothesis: the bottles of soda that were randomly selected do contain less than the desired amount of 16 ounces of soda.
(H1) Null Hypothesis: the bottles of soda do not contain less than the desired amount of 16 ounces of soda.
95% Confidence Interval (15.61, 16.09)
We are confident that the true population mean is between 15.61 and 16.09.
Margin of Error = 1.96(.67/square root of 30) = .24
P-Value = .11
Z= 15.85-16.00/0.67/(square root of 30) = -1.2246
The critical value is -1.2246
Critical Region (z/z < .8289)
Decision: since .8289 is greater than 1.2246 we accept (H0)
There is enough evidence to conclude that the mean is lower than 16 ounces.
4.
Possible causes of there being less than 16 ounces of soda are faulty machinery and inattentive workers
Issues with the adequacy of the production line. For this reason it is necessary to assign someone to monitor the production line more closely, and ameliorate the efficacy of the line.
The bottle design needs to be closely evaluate to determin if it it suitable enough to store 16 ounces of the product..
Suggestions
There should be a person or a team that is responsible for the supervision and repair of production machines to eliminate the risks of inadequate products being delivered to stores and customers.
There should also be a person or a team that is responsible for monitoring the line production to ensure that the machines are working and in compliance.
5.
The mean is calculates by adding the amount of ounces that was provided in the case study and dividing the total sum by 30. The sum of all of the values is equal to 475.62/30 =15.85
The median can be calculated by ranking the ounce values from least to greatest. Since the number is an even number you take the two innermost values and divide them by 2. In this case the values are 15.98 and 16.00. when these values are added together the total is 31.98. When divided by 2 the total is 15.49.
The mode is the value that appears the most. After evaluating the median, the mode that appears most frequently is 16.25.
The dispersion calculations consist of the variance and the standard deviation.
The variance is calculated by adding the sum of squares, which is 13.115/n-1=13.115/29 = .4522. the variance is equal to .4522.
The standard deviation is calculated as
σ = √[ ∑(x-mean)^2 / N ]
σ = √13.115/29 = √.4522 = 0.6724581771381771
6.
N=30, x = 15.85, s= .067, and z-1.96
CI = 1.96 + or – (.67/the square root of 30 or 5.47) = 15.85 + or minus .24,. the
Answer is 15.585 + .24 = 16.09, 15.85-.24 = 15.61,
95% Confidence intervals are (15.61, 16.09)
7.
The vocabulary that one must familiarize them with when conducting a hypothesis is null hypothesis, alternate hypothesis, reject, accept, Type I error, and type II error.
The null hypothesis is the a statement that indicates that an assertion about the population parameter is accurate until proven to be false
The alternate hypothesis indicates that a specified value contrast that which is proposed in the null hypothesis.
Reject means not to accept or embrace.
Accept means that the hypothesis is accurate.
Type I error occurs when rejecting the null hypothesis when it is actually true. The probability of making a type I error is α , the significance level. (Education, nd).
Type II error occurs when failing to reject the null hypothesis, when it is actually false. The probability of making a type II errors β (beta) (Education, n.d.).
8.
Hypothesis testing is applicable to a variety of professional disciplines. More specifically, in physical, and social scientist it is a common strategy used to examine relationships between variables, and the causal factors of inter correlated relationships as well.
9.
Technological tools that are useful and applicable when solving problems in statistics are computer programs such as SPSS, and Microsoft Excel. These popular tools allow researchers, mathematicians, students, and other individuals identify trends, relationships, and various other statistical components while simultaneously crunching large quantities of data.
References
Education, C. (n.d.). 9.1 Basic Principles of Hypothesis Testing. Retrieved June 2, 2016, from Cabrillo Education: http://www.cabrillo.edu/~vlundquist/math_12/9.1.pdf
