Question

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.

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

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

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

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

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

Answer 1

a ) for a = 1 - 0.956 = 0.044

Zcritical = Z_{​​​​​​a/2} = Z_{​​​​​0.022}

Zcritical = 2.0141

b) if t distribution then for a = 0.044 and d.f = n -1 = 18

tCritical = t_{​​​​​​a/2 , n-1} = t_{​​​​​​0.022,18}

tCritical = 2.1658

c) degrees of freedom = n -1 = 19 -1

Degrees of freedom = 18

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

xbar - Z​​​​​a/2*(/√n) < < xbar + Za/2 (/√n)

9.3 - 2.0141*(0.51)√19) < < 9.3 + 2.0141 *(0.51/√19)

9.06 < < 9.54