Sample Proportion Week 3 Assignment 3 Evidence
Callaway is thinking about entering the golf ball market. The company will make a profit if its market share is more than 20%. A market survey indicates that 140 of 624 golf ball purchasers will buy a Callaway golf ball.
In your initial post, answer the following questions:
- Is this enough evidence to persuade Callaway to enter the golf ball market?
- How would you make the decision if you were Callaway management? Would you use hypothesis testing?
Further explanation of what I am looking for in your responses (to help you succeed):
[I provide you this guidance to give you a better idea of what I am looking for in a distinguished level response. It is not meant to change any of the requirements from the University.] .
For this discussion, you want to determine if the market share Callaway enjoys is really greater than the 22% in their sample. Since you experience bias whenever you sample less than 100% of the population (100% sample is a census), you need to conduct a hypothesis test to determine if the sample truly reflects the population from which it is drawn. I provide you with a calculator (attached) I designed with a colleague to try and make the calculation step a bit more palatable. I welcome your comments on the format and how I can make it more user friendly.
Of course, the calculations are only one step in the decision process. Ensure you apply the appropriate amount of critical thought to your recommendation to Callaway. Include the reason why you make your recommendation.
Here is some information to help you with the discussion question.
If we measure all data points in a data set (census), the statistics we calculate are a valid representation of that population. As we discussed previously, whenever you take a sample of a population, you can expect some level of error (bias). We use the hypothesis testing process to determine if the level of bias in a sample could alter a decision we intend to make.
Based on the results of the hypothesis test we either confirm the data correctly reflects the population from which it is drawn (fail to reject Ho); or we decide the difference from the population is statistically significant (reject Ho).
When we say something is statistically significant, it means the difference we measure is greater than the statistical measure we chose. In the case of the hypothesis test, the measure is the significance level or alpha (α). For retail tests, we generally use a significance level of 0.05.
You will find most texts discuss a multiple step hypothesis testing process (five or six steps). For this discussion, I will attempt to distill the process down to the most important points. For this discussion, show all of the steps of the hypothesis testing process (below) for full credit. Make sure you attach your excel spreadsheet showing the calculations you used to arrive at your answer.
Step I: state the null (Ho) and alternative (Ha) hypotheses. I recommend you start by stating what you want to investigate as the alternative (Ha) hypothesis. The null hypothesis (Ho) is the complement of Ha and always includes the equal sign.
Step II: choose the significance level (α). The alpha you choose determines the rejection region for the problem. If the p-value you calculate in step III is less than the alpha value, you reject Ho and determine Ha to be true (difference is statistically significant). If the p-value you calculate in step III is greater than the alpha value, you fail to reject Ho and determine the difference is not statistically significant.
Step III: calculate the test statistic (p-value). This step is based on formulas you find in the text. You basically calculate the z score (t score for samples where n < 30) from the data you collected and turn that into a p-value. The calculator I attached calculates the p-value for you. You need to choose the proper type test (left tail, right tail, or two tail) to arrive at the correct answer.
Step IV: compare the p-value to alpha and make your decision to reject Ho or fail to reject Ho. Reject Ho if the p-value is less than the significance level (alpha).
* For proportions calculate the z score to determine the p-value.
* A simple way to calculate the z score for a proportion is: [(sample proportion – population proportion) / the standard error] …. or use the calculator I provided (attached).
* Use the NORMDIST function in excel to turn the Z score into a p-value.
* Do not skip any of the steps in the process. Show your work and calculations to earn full credit for this discussion question (attach your excel spreadsheet to show your work).
Hypothesis test for a proportion section 9-4 and the example (Fig 9.6; p379) in the text. I designed the attached calculator to help you complete hypothesis tests. Fill in the relevant data (yellow section) and the calculator will do the rest. Feel free to submit your work in the excel calculator to support your analysis. Copy the output from the calculator and paste (as a picture) into your excel solution (step III).
I challenge you to respond early so we can work towards the correct final answer. You can probably find solutions to this problem on the internet. Even though the answer to this problem is available on the internet, do not assume it is correct. You are to complete this problem without outside assistance. I strongly recommend you do not use outside sources to complete your work.
Let me know if you have any questions.