We would like to know whether the number of building lightening strikes per month is greater in New Hampshire or Vermont, on average. We took lightening strike data for each month of the last 3 years (36 months in all) and got the following data:

sample mean New Hampshire: 78

sample mean Vermont: 89

sample sd New Hampshire: 6.7

sample sd Vermont: 5.3

Run a test of hypothesis to test the claim that there is a difference in the population average number of lightening strikes per month in these two states at the 0.05 level, and in particular, address:

• Whether this should be considered a random sample y/n and why
• Address the other condition, and if we have enough confidence to perform the required test
• Regardless of your condition/assumptions answers above, run the test of hypothesis making sure to give:
  • Hypotheses
  • Test statistic
  • P-value
  • Decision
  • Conclusion