Question

The length of duration, in minutes, of earthquakes in California has been recorded for future analysis and information. An earthquake expert claims that the average duration of earthquakes in California is 0.5 minutes. To investigate the validity of this claim a random sample of 6 earthquakes were taken and the sample mean and the sample standard deviation were 1.15 and 0.308 minutes, respectively. Construct a 98% confidence interval and determine if the researcher`s claim can be rejected.

Group of answer choices

A) 98% C.I. is (0.855, 1.745). One cannot reject the expert`s claim that the true average duration of earthquakes in California is 0.5 minutes.

B) 98% C.I. is (0.727, 1.573). One cannot reject the expert`s claim that the true average duration of earthquakes in California is 0.5 minutes.

C) 98% C.I. is (0.855, 1.745). One can reject the expert`s claim that the true average duration of earthquakes in California is 0.5 minutes.

D) 98% C.I. is (0.727, 1.573). One can reject the expert`s claim that the true average duration of earthquakes in California is 0.5 minutes.

Answer 1

Confidence Interval
X̅ ± t(α/2, n-1) S/√(n)
t(α/2, n-1) = t(0.02 /2, 6- 1 ) = 3.365
1.15 ± t(0.02/2, 6 -1) * 0.308/√(6)
Lower Limit = 1.15 - t(0.02/2, 6 -1) 0.308/√(6)
Lower Limit = 0.727
Upper Limit = 1.15 + t(0.02/2, 6 -1) 0.308/√(6)
Upper Limit = 1.573
98% Confidence interval is ( 0.727 , 1.573 )

D) 98% C.I. is (0.727, 1.573). One can reject the expert`s claim that the true average duration of earthquakes in California is 0.5 minutes.

Because, 0.5 does not lies in the interval.