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.
a. 98% C.l.is (0.727, 1.573). One can reject the expert's claim tha thte 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 tha thte true average duration of earthquakes in California is 0.5 minutes.
c. 98% C.I. is (0.755, 1.545). One can reject the expert's claim tha thte true average duration of earthquakes in California is 0.5 minutes.
d. 98% C.I. is (0.755, 1.545). One cannot reject the expert's claim tha thte true average duration of earthquakes in California is 0.5 minutes.

Answer 1

Answer:

The answer is "(0.727, 1.573)".

Step-by-step explanation:

The confidence interval of 98 percent is C.I = (0.727, 1.573). You might disregard the statement of the experts that the genuine average duration in California of earthquakes is 0.5 minutes.

$C.I = \bar{x}\pm t_{\frac{\alpha }{2}}\times \frac{s }{\sqrt{n}}$

      $= 1.15 + 3.365 \times 0.12574\\\\= 1.15 + 0.4231\\\\= (0.7269, 1.5731)$