Question

Historically, a certain region has experienced 81 thunder days annually. (A "thunder day" is day on which at least one instance of thunder is audible to a normal human ear). Over the past seven years, the mean number of thunder days is 47 with a standard deviation of 45. Can you conclude that the mean number of thunder days is less than 81? Use the α = 0.05 level of significance.

Answer 1

H0: = 81

HA: < 81

Test Statistic :-
t = ( X̅ - µ ) / (S / √(n) )
t = ( 47 - 81 ) / ( 45 / √(7) )
t = -1.999

Test Criteria :-
Reject null hypothesis if t < -t(α, n-1)

Critical value t(α, n-1) = t(0.05 , 7-1) = 1.943
t < - t(α, n-1) = -1.999 < - 1.943

Result :- Reject null hypothesis

We have sufficient evidence to conclude that the mean number of thunder days is less than 81.