# Problem understanding what type of test to use and how to proceed with the questions provided

I have a case study where a company made new golf balls with stronger coatings than current golf balls. One of the technicians is concerned that the new coating may decrease the driving distance. An experiment was conducted in which 40 types of each ball was hit by a machine to determine mean driving distance of the two balls. The distances for each ball were given in a spreadsheet. Here are the samples:

Current: 264.00 261.00 267.00 272.00 258.00 283.00 258.00 266.00 259.00 270.00 263.00
264.00 284.00 263.00 260.00 283.00 255.00 272.00 266.00 268.00 270.00 287.00
289.00 280.00 272.00 275.00 265.00 260.00 278.00 275.00 281.00 274.00 273.00
263.00 275.00 267.00 279.00 274.00 276.00 262.00
New;     277.00 269.00 263.00 266.00 262.00 251.00 262.00 289.00 286.00 264.00 274.00
266.00 262.00 271.00 260.00 281.00 250.00 263.00 278.00 264.00 272.00 259.00
264.00 280.00 274.00 281.00 276.00 269.00 268.00 262.00 283.00 250.00 253.00
260.00 270.00 263.00 261.00 255.00 263.00 279.00


These are the questions:

1. Formulate and present the rationale for a hypothesis test that Par could use to compare the driving distances of the current and new golf balls
2. The CEO tells you (in contrast to what Bill said) that he would like to sell the new ball unless there is overwhelming evidence that the cut‐resistant ball is slower than the old ball so you should frame your hypothesis accordingly. Hint: you are more willing to make a Type II error. Analyze the data to provide the hypothesis testing conclusion and statements (at .05). Also include narrative versions of what ever of the above forms you use such as: Ho: The mean is ... What is the p‐value for your test? What is your recommendation for Par, Inc.?
3. Provide the following descriptive summaries of the data for each model: ONLY the means and variances and the z values.
4. What is the 95% confidence interval for the difference between the means of the two populations?
5. Do you see a need for larger sample sizes and more testing with the golf balls? Discuss.

I've looked for help elsewhere and everyone seems to use the t-test to conduct the analysis. Shouldn't the z-test be used since the sample sizes are both over 30? I would also like some direction in understanding how to answer the other questions but my main question is the most important.

• Is this a homework problem? If so, please add the homework tag. This is discussed in the faq, right at the top, which you may want to read. – gung - Reinstate Monica May 2 '12 at 23:24
• Please do not deface your question upon receiving a suitable answer. This site is intended to serve as a persistent store of knowledge regarding topics within its stated scope. – cardinal May 3 '12 at 20:07

With respect to your main question, there is no 'bright line' between small $N$ and large $N$, not at 30, 50 or 100 (where most tables stop before jumping to $\infty$). If you are estimating the SD from your data, the t-test is appropriate. After a certain point, the results you get will be indistinguishable from a z-test, but from a theoretical perspective, the t-test remains appropriate.