MAT3000 Statistics Homework: Soda Bottle Weight Analysis & Testing

This statistics assignment, focusing on MAT3000, examines customer complaints regarding soda bottle weights. The student analyzed a sample of 30 soda bottles, calculating descriptive statistics such as mean and standard deviation, and constructed a 95% confidence interval for the mean weight. Hypothesis testing was performed to determine if the average weight of the bottles was equal to 16 ounces, using a one-sample t-test. The analysis revealed that although the sample mean was less than 16 ounces, the null hypothesis could not be rejected, indicating that the claim of underweight bottles was not strongly supported. Recommendations were made to reduce variability in the bottling process, including addressing assignable causes, correcting machine errors, and retesting material quality to ensure customer satisfaction and maintain the company's reputation. The assignment includes tables of statistical data, the t-test results, and references to relevant statistical resources.

Running head: MAT3000: STATISTICS
MAT 300: Statistics
Name of the Student:
Name of the University:
Author’s note:

1MAT3000: STATISTICS
Table of Contents
Introduction:...............................................................................................................................2
Analysis:.....................................................................................................................................2
Answer 1................................................................................................................................2
Answer 2................................................................................................................................2
Answer 3................................................................................................................................2
Answer 4................................................................................................................................3
References:.................................................................................................................................5
Appendix:...................................................................................................................................6

2MAT3000: STATISTICS
Introduction:
It is a topic of concern that as per as the complaint of customers, the weight of soda bottle is
less than 16 ounces or not. For examining the complaint of the customers, we have drawn a
sample of 30 bottles at random from all the shifting at the bottling plant. The measurements
of weights of soda from all the soda bottles are tabulated and used for analysis. After
analysing data, we would draw the necessary conclusions.
Analysis:
Answer 1.
Table 1: Descriptive Statistics of weights of soda bottles
The mean weight of soda bottles is 15.854 ounces, median weight of soda bottles is 15.99
ounces and standard deviation of soda bottles is 0.661381 ounces. The mean weight infers
that the weight of soda bottles is less than 16 ounces whereas the standard deviation of
0.6614 ounces indicates that the spread of weight of soda bottles is insignificant.
Answer 2.
Table 2: Table of 95% confidence intervals of mean weight of soda bottles
We prefer to find confidence intervals of mean weights of soda bottles at 5% level of
significance. The upper confidence limit of the mean weight of soda bottles is 16.09 ounces
and lower confidence limit of the mean weight of soda bottles is 15.62 ounces
(Onlinestatbook.com, 2018).
Answer 3.
The hypotheses for testing is-

3MAT3000: STATISTICS
Null hypothesis (H0): The average weight of sampled soda bottles is equal to 16 ounces.
Alternative hypothesis (HA): The average weight of sampled soda bottles is less than 16
ounces.
Table 3: One sample t-test of weights of soda bottles
Table 4: Table for decision making
The calculated t-statistic is (-1.2091).
 At 5% level of significance, the two-tailed t-statistic = 2.04523 (t-critical). As, tcrit>tcal,
therefore, we cannot reject the null hypothesis of equality of mean weight of 16
ounces (Lowry, 2014). Hence, there exists the significant equality of weights of soda
bottles of 16 ounces.
 From the calculated t-statistic, we find the p-value = 0.236391. As, the p-value is
greater than critical p-value that is 0.05, therefore, we accept the null hypothesis of
equality of weight of soda bottles 16 ounces. From this approach also, there exists the
significant equality of weights of soda bottles of 16 ounces.
Answer 4.
From the analysis, it is found that mean weight of 30 soda bottles is less than the expected
mean weight. However, it is 95% evident from the hypothesis testing that soda bottle weighs

4MAT3000: STATISTICS
16 ounces. The claim of consumers is not strongly valid. Although, to minimize spread in
terms of standard deviation, we should concentrate on-
 Decrement of the assignable causes arisen of soda factory from manpower and
environment
 The correction of error of soda generating machine and weight measuring units
(Jiang, 2015).
 Rectification the method of soda generation and retesting the quality of material of
soda.
As the spread of the weights of soda bottles would decrease after taking the possible measure,
the weights of soda bottles would be very near to 16 ounces (iSixSigma., 2018).
Consecutively, the customer satisfaction would increase and reputation of company would be
maintained.

5MAT3000: STATISTICS
References:
Common Cause Variation | iSixSigma. (2018). Isixsigma.com. Retrieved from
https://www.isixsigma.com/dictionary/common-cause-variation/
Confidence Interval for the Mean. (2018). Onlinestatbook.com. Retrieved from
http://onlinestatbook.com/2/estimation/mean.html
Jiang, R. (2015). Product Quality Variations and Control Strategies. In Introduction to
Quality and Reliability Engineering (pp. 221-234). Springer, Berlin, Heidelberg.
Lowry, R. (2014). Concepts and applications of inferential statistics.

6MAT3000: STATISTICS
Appendix:
The control chart of the sampled products indicates the violations of two samples out of 30
samples according to moving range of the weights of samples.