A seismologist recorded the following earthquake depths in k

A seismologist recorded the following earthquake depths in km.

6.6           2.2           18.5        7.0           13.7        5.4           5.3           5.9           4.7           14.5        3.2           9.1           8.0

15.3        5.6           10.0        8.2           8.2           9.9           13.7        14.8        15.1        16.3        8.6           3.3           5.6

1.Using Minitab, determine the 99% confidence interval estimate. (3 points)

2.Write a confidence statement for your confidence interval estimate. ( 5 points)

3. Based on our confidence interval estimate can we safely say that the mean depth for all earthquakes will be at most 10 km? Please give a reason for your answer. (5 points)

Solution

1.

Note that              
              
Lower Bound = X - t(alpha/2) * s / sqrt(n)              
Upper Bound = X + t(alpha/2) * s / sqrt(n)              
              
where              
alpha/2 = (1 - confidence level)/2 =    0.025          
X = sample mean =    9.180769231          
t(alpha/2) = critical t for the confidence interval =    2.059538553          
s = sample standard deviation =    4.612679848          
n = sample size =    26          
df = n - 1 =    25          
Thus,              
              
Lower bound =    7.31766752          
Upper bound =    11.04387094          
              
Thus, the confidence interval is              
              
(   7.31766752   ,   11.04387094   ) [ANSWER]

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b)

We are 95% confident that the true mean earthquake depth is between 7.3177 km and 11.0439 km. [ANSWER]

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c)

No, because part of the interval is greater than 10 km. [ANSWER]