# Hypothesis testing problems

1) Test equally likeliness of random numbers.

a. Use Excel to generate 500 random digits per the instructions below.

1. Click on fx and from the Math&Trig category, choose RANDBETWEEN and click OK.

2. In the bottom of the dialog box enter 0 and in the top enter, then click OK. This tells Excel to generate digits between 0 and 9.

3. Highlight cells A1 through A500 so you get 500 digits generated.

4. You can record these results in a table such as you did previously for a histogram with the Excel "bin" feature. In column B enter the values 0-9 in

the first 10 rows. How use Histogram in Data Analysis to generate a

frequency table to better see the results.

b. Use a significance level of 0.05 to test the claim that your sample of digits come from a population where all digits are equally likely. Report on whether or not Excel is properly generating random numbers. Make sure to show all our work in the submitted spreadsheet.

2) Test for the same mean. See at the attached Words.xls data file for this part of the project.

a. Test the null hypothesis that the six samples of word counts for males (odd columns ending in M) are from a population with the same mean.

b. Test the null hypothesis that the six samples of word counts for females (even columns) are from a population with the same mean.

c. If we want to compare the number of words spoken by men to the number spoken by women, does it make sense to combine the six columns to word counts for males and the same for females before then comparing?

d. Make a report that addresses each of parts a-c above and justify your answers.

3) Testing Random Numbers by nonparametic methods.

a. Use the random numbers created in part 1) above and test for randomness using three of the methods in chapter 13. Again, show all work and report on the findings of each.

4) Quality control process testing. Again, use the RANDBETWEEN function in Excel. This time generate 200 random numbers between 1 and 100 and output it to one column. Then do the same for until you have 20 columns of which are 200 in length that all have values between 1 and 100.

a. The above generated data is to simulate 20 days of a quality control process. Consider an outcome of 1-5 to be a defect and an outcome of 6-100 to be an acceptable result. Note that this corresponds to a 5% rate of defects.

b. Construct a p chart for the proportion of defective calculators, and determine whether the process is within statistical control. The process is stable with p = 0.05 so a conclusion that it is not stable would be a type I error which means we would have a false positive signal causing use to think that the process should be adjusted when, in fact, it was fine.

c. Simulate another 10 days of manufacturing calculators (as in part a), but modify these 10 so that the defect rate is 10% instead of 5%.

d. Combine the data from parts a) an c) to represent a total of 30 days of results. Construct a p chart for this combined sample. Is the process out of control or not? If we conclude it is not, we would make a type II error which means that we would believe the process was fine when it should be adjusted to correct the 10% rate of defects.

e. Again, make all your data presentable and report on your findings.

#### Solution Summary

Step by step method for computing test statistic is given in the answer.