Question

According to the U.S. National Weather Service, at any given moment of any day, approximately 2000 thunderstorms are occurring worldwide. Many of these storms include lightning strikes. Sensitive electronic equipment is used to record the number of lightning strikes worldwide every day. 28 days were selected at random, and the number of lightning strikes on each day was recorded. The sample mean was 8.3 million. Assume the distribution of the number of lightning strikes per day is normal and has a population standard deviation of 0.45 million. Please use 4 decimal places for all critical values.

a) What assumptions are required so that you can construct a confidence interval for the mean number of lightning strikes per day?

b) Should you use a z distribution or a t distribution in this problem? Note that you will only get one try to get this question correct. Please explain the correct answer.

c) Find the 97.5% confidence interval for the true mean number of lightning strikes per day. (just write the answer, no need solution)

c) i) If this would be a z distribution, what would be the critical value? Please use 4 decimal places.

c) ii) If this would be a t distribution, what would be the critical value? Please use 4 decimal places.

c) iii) If this would be a t distribution, what would be the degrees of freedom?

c) vi) The 97.5% confidence interval for the true mean number of lightning strikes per day is

( , )

Answer 1

a) The assumptions are:

The samples are simple random samples.

The population is normally distributed.

The population standard deviation is known.

b) We should use z-distribution since the population standard deviation is known.

c)i) At 97.5% confidence level, the critical value is z* = 2.24

ii) tcrit = 2.373

iii) Degrees of freedom = 28 - 1 = 27

iv) The 97.5% confidence interval is

+/- z* *

= 8.3 +/- 2.24 * 0.45/

= 8.3 +/- 0.19

= 8.11, 8.49