Business Research Problem Introduction The statistical analysis plays an important role in the decision making for so many business industries. In the pharmaceutical companies the study of the different parameters regarding the medicine is very important. We use different statistical methods for the study of these variables or parameters regarding the medicines or drugs. The management team of the well known medicine company wants to claim regarding the different tablets they made. Let us see this study in detail given as below: Research Question For any business research study, it is very important to establish the research question which gives proper direction and guidelines for research study. The management team of the medicine company wants to check the following claim or hypothesis. Whether the average weight of the tablet is 0.75 Milligrams or not? Whether the average concentration of the sodium content in each tablet is 2% or not? For checking these claims we need to collect the data. The data collection process with collected data is explained in the next topic. Data Collection The management team of the medicine company wants to check the above stated claims and therefore they collect the data for 50 tablets. The team uses the random sampling method for the collection of the data. The collected data for the weight of the tablet and sodium concentration of the tablet is given as below: No. 1 2 3 4 5 6 7 8 9 10 Weight mg 0.7493 0.7499 0.7494 0.7497 0.75 0.7495 0.7492 0.7508 0.7492 0.7493 Sodium concentration % 1.992 1.998 1.992 1.999 2 1.99 2.003 1.995 2.002 2.01 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 0.7508 0.749 0.7503 0.7505 0.7505 0.7498 0.7497 0.7508 0.7505 0.7496 0.7505 0.7507 0.7508 0.7499 0.7507 0.7497 0.751 0.7506 0.7507 0.7491 0.7494 0.751 0.7499 0.7506 0.75 0.7509 0.751 0.7497 0.7507 0.751 0.7494 0.751 0.7499 0.7503 0.749 0.7498 0.7499 0.7493 0.7509 2.009 2.005 2.005 1.997 1.991 2.008 2.006 1.99 1.999 1.993 2.006 1.994 2 1.998 2.002 1.99 2.004 1.99 2.003 2.01 2.008 2.007 2.001 1.993 1.995 2.001 2.002 1.993 2.003 1.992 2.007 1.995 2.006 2.009 2.01 2.006 1.998 2.007 1.998 50 0.7493 1.993 Statistical Analysis Here, we have to see the statistical analysis by using the different statistical tools and methods. We have to use the descriptive statistics and inferential statistics for this analysis. The descriptive statistics for given two variables are summarized as below: Weight Mean 0.75009 Standard Error Median Mode Standard Deviation Sample Variance Kurtosis Skewness Range Minimum Maximum Sum Count 9.18406E-05 0.74995 0.7499 0.000649411 4.21735E-07 -1.418451667 -0.065433668 0.002 0.749 0.751 37.5045 50 Sodium concentration Mean 2.0001 0.00090 Standard Error 2 Median 2.0005 Mode 1.998 Standard Deviation 0.00638 Sample Variance 4.07E-05 Kurtosis -1.2772 Skewness -0.08934 Range 0.02 Minimum 1.99 Maximum 2.01 Sum 100.005 Count 50 For the collected sample of 50 tablets we get the average weight of the tablet as 0.75009 milligrams with standard deviation of 0.00065 Milligrams. Also, the average sodium concentration for the given 50 tablets is observed as 2.0001% with the standard deviation of 0.006%. Now, we have to check the given two claims by using the one sample t test for the population mean. First of all we have to check the claim whether the average weight of the tablet is 0.75 Milligrams or not. The t test for checking this claim is summarized as below: t Test for Hypothesis of the Mean Data Null Hypothesis = 0.75 Level of Significance 0.05 Sample Size 50 Sample Mean 0.75009 Sample Standard Deviation 0.00064941 1 Intermediate Calculations Standard Error of the Mean 0.0001 Degrees of Freedom 49 t Test Statistic 0.9800 Two-Tail Test Lower Critical Value -2.0096 Upper Critical Value 2.0096 p-Value 0.3319 Do not reject the null hypothesis Now, we have to check another claim whether the average concentration of the sodium content in each tablet is 2% or not. For checking this claim we have to use the one sample t test for population mean which is given as below: t Test for Hypothesis of the Mean Data Null Hypothesis = 2 Level of Significance 0.05 Sample Size 50 Sample Mean 2.0001 0.00637997 Sample Standard Deviation 5 Intermediate Calculations Standard Error of the Mean 0.0009 Degrees of Freedom 49 t Test Statistic 0.1108 Two-Tail Test Lower Critical Value -2.0096 Upper Critical Value 2.0096 p-Value 0.9122 Do not reject the null hypothesis Now, for the above statistical analysis, the interpretations and conclusions are given as below: Interpretations and Conclusions For the collected sample of 50 tablets we get the average weight of the tablet as 0.75009 milligrams with standard deviation of 0.00065 Milligrams. Also, the average sodium concentration for the given 50 tablets is observed as 2.0001% with the standard deviation of 0.006%. For the t test regarding the average weight of the tablet, we get p-value as 0.3319 which is greater than alpha value 0.05, so we do not reject the null hypothesis that the average weight of the tablet is 0.750 milligram. For the t test regarding the average concentration of the sodium we get the p-value as 0.9122 which is greater than the given level of significance or alpha value 0.05, so we do not reject the null hypothesis that the average sodium concentration of the tablets is 2%. References Antony, J. (2003). Design of Experiments for Engineers and Scientists. Butterworth Limited. Babbie, E. R. (2009). The Practice of Social Research. Wadsworth. Beran, R. (2000). React scatterplot smoothers: Superefficiency through basis economy. Journal of the American Statistical Association. Bickel, P. J. and Doksum, K. A. (2000). Mathematical STatistics: Basic Ideas and Selected Topics, Vol I. Prentice Hall. Casella, G. and Berger, R. L. (2002). Statistical Inference. Duxbury Press. Cox, D. R. and Hinkley, D. V. (2000). Theoretical Statistics. Chapman and Hall Ltd. Degroot, M. and Schervish, M. (2002). Probability and Statistics. Addison - Wesley. Dobson, A. J. (2001). An introduction to generalized linear models. Chapman and Hall Ltd. Evans, M. (2004). Probability and Statistics: The Science of Uncertainty. Freeman and Company. Hastle, T., Tibshirani, R. and Friedman, J. H. (2001). The elements of statistical learning: data mining, inference, and prediction: with 200 full-color illustrations. Springer - Verlag Inc. Hogg, R., Craig, A., and McKean, J. (2004). An Introduction to Mathematical Statistics. Prentice Hall. Liese, F. and Miescke, K. (2008). Statistical Decision Theory: Estimation, Testing, and Selection. Springer. Business Research Proposal Report Introduction The world of business industry increasing day by day and there is a tough competition between the different business industries. There are so many changes in the system of management and decision making. The use of statistical methods becomes necessary for every industry for improvement of the quality of the products and optimization of the revenue of the industry. We want to study the use of different statistical methods and techniques in the pharmaceutical industry. In pharmaceutical industry different methods for quality control are required to maintain the process. We want to study the business research problem associated with one of the pharmaceutical industry regarding the production of the medicines and drugs. The management company wants to check different claims regarding the parameters associated with drugs or medicines. Let us see this business research proposal in detail. Research Question We know that it is important to develop the research question for any business research study. The research question or hypothesis for this business research study would be developing as below: Whether the average weight of the tablet is 0.75 Milligrams or not? Whether the average concentration of the sodium content in each tablet is 2% or not? Now, for checking these research hypothesis or research questions we need to collect the data or sample. Let us see the process of the data collection for this research study. Data Collection For checking the above claims or research questions for this research study we would collect the data for the two variables weight in mg and sodium concentration in percentage. For this purpose we would collect the sample of the at least 100 tablets and then collect the information for the weight of the tablet in mg and sodium concentration of the tablet. We would select the sample of at least 100 tablets by using the random sampling technique. We would use the proper measurement system while taking the readings. We would avoid any type of errors during the time of data collection which would produce the biased results for the research study. After collection of this data we would analyze this data by using the different methods of statistical tools and techniques. Statistical Analysis For the analysis of the collected data for checking the research hypothesis we have to use the different statistical tools and techniques. First of all we use the descriptive statistics for the given two variables weight of the tablet in mg and sodium concentration in percentage. We would calculate the mean, mode, median, standard deviation, range, variance, skewness, kurtosis, etc for the given two variables weight of the tablet in mg and sodium concentration in percentage. This descriptive statistics would give us the general idea about the nature of the data and distribution of the data for the given two variables weight of the tablet in mg and sodium concentration in percentage. We would also use some graphical analysis for the given two variables weight of the tablet in mg and sodium concentration in percentage. We would produce the histogram and box plots for the weight of the tablet in mg and sodium concentration in percentage. These histograms and box plots would help us for understanding the nature of the data for the given two variables weight of the tablet in mg and sodium concentration in percentage. Now, for checking the given claims for this research study, we would use the one sample t test for the population mean. For this test we would develop the null and alternative hypothesis as below: Null hypothesis: H0: The average weight of the table is 0.75 mg. Alternative hypothesis: Ha: The average weight of the tablet is different than 0.75 mg. H0: = 0.75 mg versus Ha: 0 This is a two tailed test or non-directional test. Then we would find the test statistic value and p-value for this test and then by comparing the pvalue with the given level of significance or alpha value, we would take the proper decision by using the decision rule. After checking this claim, we would check another claim whether the average concentration of the sodium content in each tablet is 2% or not. For checking this claim we would use the sample one sample t test for the population mean. The null and alternative hypothesis for this would be given as below: Null hypothesis: H0: The average percentage of the sodium concentration is 2% Alternative hypothesis: Ha: The average percentage of the sodium concentration is not 2%. H0: = 2% versus Ha: 2% This is a two tailed test. We would decide the level of significance or alpha value for this test as the 5% or alpha = 0.05. Then we would find the test statistic value and P-value. Then we would use the decision rule for rejecting or do not rejecting the null hypothesis for this test. Interpretations and Conclusions After this statistical analysis, we would find out the descriptive statistics for the given two variables weight in mg and sodium concentration in percentage. We would find the descriptive statistics as the mean, mode, median, standard deviation for these two variables. We would interpret these two variables based on the values we get for these variables. After conducting the one sample t tests for the population mean for checking the given claims or research hypothesis we would take the proper decisions by using the decision rule for the p-value approach. We would reject the null hypothesis if the p-value is less than then given level of significance or alpha value and we would not reject the null hypothesis if the p-value is greater than the given level of significance or alpha value. References Antony, J. (2003). Design of Experiments for Engineers and Scientists. Butterworth Limited. Babbie, E. R. (2009). The Practice of Social Research. Wadsworth. Beran, R. (2000). React scatterplot smoothers: Superefficiency through basis economy. Journal of the American Statistical Association. Bickel, P. J. and Doksum, K. A. (2000). Mathematical STatistics: Basic Ideas and Selected Topics, Vol I. Prentice Hall. Casella, G. and Berger, R. L. (2002). Statistical Inference. Duxbury Press. Cox, D. R. and Hinkley, D. V. (2000). Theoretical Statistics. Chapman and Hall Ltd