Discuss the below:
Q: What is the mean number of rolls of a die before a 1 is observed? Roll a die until a 1 is observed. Repeat this process 30 times and answer the following questions.
1. Obtain a point estimate of the mean number of rolls of a die before a 1 is observed.
2. The population standard deviation for the number of rolls before a 1 is observed. Use this result to construct a 90% Z-interval for the mean number of rolls required before a 1 is observed.
3. The population mean number of rolls before a 1 is observed is 6. Does your interval include 6? What proportion of the Z-intervals in the class included 6? How many did you expect to include 6?
4. Construct a 90% t-interval for the mean number of rolls required before a 1 is observed.
5. The population mean number of rolls before a 1 is observed is 6. Does your interval include 6?
6. What proportion of the t-intervals in the class includes 6? How many did you expect to include 6?
7. Compare the Z-interval with the t-interval. Which has the smaller margin of error