(Answered) Evaluate how a one-sample hypothesis test could be used to determine

1. Evaluate how a one-sample hypothesis test could be used to determine whether there are performance issues where you work (current or former job) or where you go to school. Support your response with a specific example and references.
2. The normal variance for filling a liter Coke bottle is 0.5 ounces. In a recent measurement, variance was found to be 0.8 ounces. Should Coca-Cola’s management be concerned? Discuss why or why not and include references to support your reasoning.
3. Write the null and alternative hypotheses for a right-tailed hypothesis test of variance related to your field of interest. Give each hypothesis in mathematical terms and also state in written terms. Discuss the possible outcomes and what happens if the null hypothesis is rejected. Be sure to include references.
4. Describe the importance of the chi-squared goodness of fit test. How is the goodness of fit test different from the tests for independence? Provide a goodness of fit example that would be relevant to your life and use references to explain how the test is used to evaluate data.
5. Your mayor just announced that the local unemployment rate dropped from 10.5% to 10.4% from the prior month. Use hypothesis testing to evaluate the unemployment rate drop and discuss whether there is enough information to determine statistical significance. Which hypothesis test would you use? What additional information would you need, if any? Support your response with specific examples and references.
6. Research, copy, and paste a simple regression Excel output that includes the ANOVA table and the values for r, r2, b0, and b1. Determine whether you should accept or reject the null hypothesis if the alpha value was 0.05. Write down the resultant regression equation. Be sure to reference your sources.
7. You have a regression equation based on data from years 1 thru 10 (y = 6 + 32x, where x equals year). You want to forecast a result in Year 20. How would you do it? Discuss the potential pitfalls. Be sure to include relevant references.

Sample Answer

Discussion Questions

Question G

Evaluate how a one-sample hypothesis test could be used to determine whether there are performance issues where you work (current or former job) or where you go to school. Support your response with a specific example and references

A possible example for hypothesis testing that could be calculated to determine player performance issues would be to test the players’ efficiency rating in the NBA using a greater than or less than the scale to decide top tier and bottom tier players. These numbers might change how a team thinks about who they look for in a free agency to bolster their roster. The very best PER (Player Efficiency Rating) of active players is Giannis Antetokounmpo at 31.94. The lowest is Terrance Ferguson, at 3.71. The mean of player PER is 17.825. A general manager could find value in players that have a better PER but are not the well-known names in the league.

For example, this could determine a player’s value to a team if they are a free agent. As an NBA fanatic, I can tell you that every team would rather have Pascal Siakam with a PER 17.96 over Mason Plumlee, who has a PER of 18.86. Now, the PER does not consider a player’s athleticism, just how efficient the player is with adding positive stats then subtracting negative stats measured by the amount of playing time they get. A GM could use hypothesis testing to compare how any given player will raise their PER on their given team based on the team’s style of play. So, suppose a player has not been afforded the playing time they need to develop because they have one or two players in front of them, taking time away, and your team does not have that log jam at the player’s position. In that case, you could potentially raise the PER of the said player quite a bit by measuring the PER based on your teams’ style of play and the player’s change in playing time measured against the average PER, 17.825. This could shake out performance issues of current players on your team and help you decide on one free agent over another.

I am pretty sure all teams are already doing this.

Reference

• Anderson, D. R., Sweeney, D. J., Williams, T. A., Camm, J. D., & Cochran, J. J. (2021). Essentials of Modern Business Statistics with Microsoft Office Excel (8th ed.). Cengage. ISBN-13: 9780357131664

Question H

The normal variance for filling a liter Coke bottle is 0.5 ounces. In a recent measurement, the variance was found to be 0.8 ounces. Should Coca-Cola’s management be concerned? Discuss why or why not and include references to support your reasoning.

There is a reason that Coca-Cola has an established normal variance. It is a data-driven variance that ensures optimal profitability and realistic variance expectations. If the normal variance is 0.5, then you could expect variances above and below 0.5 as well. The same can be said for the current variance of 0.8. So, Coke could potentially miss filling bottles up to a full ounce on either side of the spectrum. Not only could that variance severely affect Coke’s revenue but also affect the employees. This unaccounted-for loss in revenue might affect raises and bonuses that employees have enjoyed for years.

A company as big as Coca-Cola could see hundreds of thousands to millions of dollars in lost revenue over a 0.3 difference in normal variance. Another factor that has always been important to me in a big brand such as Coke is consistency. An ice-cold Coca-Cola has tasted the same to me from the first bottle I tasted to the last bottle I had a week ago. If Coke’s variance level of filling bottles has changed, there is also a chance that quality could be affected as well. Coke sells on average $1.7 billion in products daily. An astronomical amount of product! That number leaves a paper trail of finely tuned decisions; it is not achieved by accident. Management should be very concerned with the variance increase. Coke’s meticulous manufacturing process and variance acceptance are not arrived at by accident. This issue needs to be investigated and resolved as soon as possible. Coke cannot accept a variance that could cost them millions.

Reference

• Anderson, D. R., Sweeney, D. J., Williams, T. A., Camm, J. D., & Cochran, J. J. (2021). Essentials of Modern Business Statistics with Microsoft Office Excel (8th ed.). Cengage. ISBN-13: 9780357131664

Question I

Write the null and alternative hypotheses for a right-tailed hypothesis test of variance related to your field of interest. Give each hypothesis in mathematical terms and also state it in written terms. Discuss the possible outcomes and what happens if the null hypothesis is rejected. Be sure to include references.

Right tailed hypothesis depicts a greater than symbol show as >. I remember by saying the alligator eats the bigger number. It is silly, but it works. To put the right hypothesis simply, the data is in favor of the right. My example would be the latest marketing campaign of a product to new markets and expecting to sell it for $100. After the initial launch, we see that the price is too high and the manufacturing cost for the product is too high to make a reasonable profit for success. So, if we decide that the price of the product needs to be $80 based on the cost of each sale, then we randomly pick the cost of the sale in 10 randomly selected regions is $75. Then we determine the standard deviation of $10.

Our test would be;

On average, the price of the product is less than $80

On average, the price of the product is greater than $80

Assuming .05 is the alpha. The Z score is 0.5.

In this case, I would reject the hypothesis since there is sufficient evidence to support the alternative hypothesis. I believe we should tone down our sales expectations or adjust the price to accommodate the loss we have already incurred.