# mathematics

Answer the questions with CITATION and Reference NO PLAGIARISM.

No more 400 words.

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This unit we are using simulation models to investigate the behaviour of critical performance variables, such as profit, in the presence of uncertainty. We use statistical analysis, primarily sample means and standard deviations, to investigate the properties of the simulated value. Underlying our ability to use statistical analysis techniques on the simulated values is the Central Limit Theorem.

1-Why is the Central Limit Theorem so important to statistical analysis?

2-How does the Central Limit Theorem help us when we are testing hypotheses about sample means?

3- Reflect on what happens to the shape of a graph when the number of samples increases and number of data in each sample increases – i.e., how does an increase in sample affect the distribution mean and standard deviation?

4- Try to relate ideas in this discussion to the analysis of results from simulation models.

response comment on each other’s graph discussion and contribute your perspective and analysis for the chosen graph.

1.An experiment was performed on a certain metal to determine if the strength is a function of heating time (hours). Results based on 20 metal sheets are given below. Use the simple linear regression model.

∑X = 40

∑X^{2} = 200

∑Y = 70

∑Y^{2} = 545

∑XY = 320

Find the estimated y intercept and slope and write the equation of the least squares regression line. Estimate Y when X is equal to 3 hours. Also determine the standard error, the Mean Square Error, the coefficient of determination and the coefficient of correlation.

2. Use the following results obtained from a simple linear regression analysis with 15 observations.

YHat= 35.5- (1.25)X

R^{2}= 0.8745 and s_{b1 }= 0.50

Interpret regression results and the value of the coefficient of Determination. Predict the value of Y when X is equal to 10. Calculate the correlation coefficient between Y and X. Test to determine if there is a significant relationship between the independent and dependent variable at a = 0.05. Perform a two-tailed test.