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Confidence intervals and hypothesis testing? Maybe?

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A local merchant is interested in obtaining a small business loan to expand his business. He will be able to obtain a more favorable interest rate if he can reasonably demonstrate that his near-term monthly revenues will be between $10,000 and $15,000. He doesn't know the exact level of sales to expect over the next several months, but based on past experience, he knows it should be around $13,000. He also knows that his sales vary by about $2,500 from month to month. What is the probability that his store will generate the revenue required for him to obtain a favorable loan rate?

Use one of the following to address
-Confidence intervals and hypothesis testing
-Decision trees (and their use in solving managerial problems),
-Critical fractile analysis (and its use in determining optimal demand levels),
-Analysis of variance/ANOVA (and its use in understanding differences between group means),
-Chi-square (cross tabs/contingency table) analysis (and its use in determining differences between group proportions),
-Regression, single and multiple (and its use in understanding relationships between dependent and independent (explanatory) variables), and
-Optimization modeling (and its use in determining the best solution given a set of constraint).

How to approach this? Help!!!!!!

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Solution Preview

This is a normal distribution problem:
<br>His average revenue is 13000, and standard deviation is 2500
<br>Then we are to find the probability that next ...

Solution Summary

The solution addresses a local merchant is interested in obtaining a small business loan to expand his business. He will be able to obtain a more favorable interest rate if he can reasonably demonstrate that his near-term monthly revenues will be between $10,000 and $15,000. He doesn't know the exact level of sales to expect over the next several months, but based on past experience, he knows it should be around $13,000. He also knows that his sales vary by about $2,500 from month to month. What is the probability that his store will generate the revenue required for him to obtain a favorable loan rate?

Use one of the following to address
-Confidence intervals and hypothesis testing
-Decision trees (and their use in solving managerial problems),
-Critical fractile analysis (and its use in determining optimal demand levels),
-Analysis of variance/ANOVA (and its use in understanding differences between group means),
-Chi-square (cross tabs/contingency table) analysis (and its use in determining differences between group proportions),
-Regression, single and multiple (and its use in understanding relationships between dependent and independent (explanatory) variables), and
-Optimization modeling (and its use in determining the best solution given a set of constraint).

$2.19
See Also This Related BrainMass Solution

Statistical Processes for Hypothesis Testing

(See attached file for full problem description with proper equations)

An engineer was interested in comparing the variability of the power of a laser at current levels of 16 amps (X) and 20 amps (Y). To do so, random samples of 25 observations of power readings were obtained at each current level. The samples were taken hi such a manner that independence could be assumed.
Sample variances of 0.012 and 0.020 were obtained for X and Y, respectively. That is, the sample observations resulted in sx2 =0.012 and sY2 =0.020 . Also, the data indicated that the sampled populations were normally distributed.

a. Find a 95% confidence interval for the variance of X, x2.
b. Find a 95% confidence interval for the variance of Y, Y2
c. Find a 95% confidence interval for the ratio of the variances of X and Y,
d. Can you conclude that the respective variances of power at each of the two current levels may be the same? Are your results for parts a, b and c consistent. Explain your answer fully.

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