Question

a) According to the U.S. National Weather Service, at any given moment of any day, approximately 1000 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. 19 days were selected at random, and the number of lightning strikes on each day was recorded. The sample mean was 9.3 million. Assume the distribution of the number of lightning strikes per day is normal and has a population standard deviation of 0.51 million. Please use 4 decimal places for all critical values.

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.

c) Please explain the correct answer.

d) Find the 95.6% confidence interval for the true mean number of lightning strikes per day.

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

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

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

iv) The 95.6% confidence interval for the true mean number of lightning strikes per day is

e) Interpret your answer from the interval above (part d)

f) Please show all of the code for this part (part d) below.

g) Determine the number of days that need to be sampled to ensure that the half-width of the interval in b) is at most 0.19 million. Assume a confidence level of 95.6% Please use at least 4 decimal places in all numbers used (unless the number is exact). What is the new sample size?

h) Please show all of the code for this part (part g) below

i) In a previous year, the number of measured lightning strikes world wide was 9.11 million. Do you think that the number of lightning strikes has changed from 9.3 million? Please explain your answer

Answer 1

(b) z distribution.

(c). Since we assume that the distribution of the number of lightning strikes per day is normal and has a population standard deviation of 0.51 million so we use z distribution.

d) Find the 95.6% confidence interval for the true mean number of lightning strikes per day.

i) If this would be a z distribution, the critical value=z0.022=2.0141

iv) The 95.6% confidence interval for the true mean number of lightning strikes per day is (9.0643,9.5357).

e) We are 95.6% confident that the true mean number of lightning strikes per day lies in (9.0643,9.5357).

(f)

R code:

cr=round(qnorm(1-0.022),4)# critical value
n=19 #sample size
m=9.3 #sample mean
sigma=0.51 #population sd
LB=round(m-cr*sigma/sqrt(n),4)# lower limit of CI
UB=round(m+cr*sigma/sqrt(n),4)#upper limit of CI
LB
UB

(g)

(i) Since 9.11 million lies in 95.6% confidence interval: (9.0643,9.5357) so we do not think that the number of lightning strikes has changed from 9.3 million.