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

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.

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.

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.

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.

Answer 1

Given: population mean(μ)= 0.5 sample standard deviation(s)=0.308 sample mean(x̄) = 1.15  sample size(n) = 6.0  level of significance = α = 0.02  Degrees of freedom = n-1 = 5.0 critical value =3.3649  Confidence Interval:  x̄ ± t(α/2,df)(s/√n) = 1.15 ± (3.3649)(0.308/√6.0) = 1.15 ± 0.4231 implies ( 0.7269 , 1.5731 ) lower bound = 0.7269  upper bound = 1.5731 Conclusion: 98% C.I is ( 0.727 , 1.573 ). one can reject the experts claim that the true average duration of earthquakes in california is 0.5 minutes.