From a list of all passengers onboard at the time of the col

From a list of all passengers onboard at the time of the collision, groups were formed with ten names in each group. Then three of these groups were were selected using simple random sampling without replacement. The thirty passengers from the three selected groups are in the table below. Cells with an * indicate that this information is not known.

For the remaining questions, assume that the dataset was obtained using simple random sampling without replacement. Base your answers ONLY on the dataset… Please show all work for each question.

A) Calculate with 99% confidence the upper bound of the proportion (correct to three decimal places) of all passengers that boarded at Cherbourg.

B) Calculate with 95% confidence the mean age (correct to three decimal places) of all passengers.

C) How many randomly selected passengers would have to be selected to estimate the number that boarded at Cherbourg to within five persons with 95% confidence?

D) How many randomly selected passengers would have to be selected to estimate the age of all passengers to within five years with 90% confidence?

E) At a 5% significance level, is there evidence that at most half of the passengers survived?

Please show all steps, including both the CV and p-value

F) At a 10% significance level, is there evidence that the mean age of all of the passengers is less than 27?

Please show all steps, including both the CV and p-value

9 AGE LASTNAME FIRSTNAME Bucknell 1 2 Crosby heim Beniamin Female Corbett 9 Norman Padron-Manent Julian 2 2 Constance Williams Queenstown Queenstown 3 Devaney

Solution

A.

Note that              
              
p^ = point estimate of the population proportion = x / n =    0.3          
              
Also, we get the standard error of p, sp:              
              
sp = sqrt[p^ (1 - p^) / n] =    0.083666003          
              
Now, for the critical z,              
alpha/2 =   0.005          
Thus, z(alpha/2) =    2.575829304          
Thus,              
          
upper bound = p^ + z(alpha/2) * sp =    0.515509341 [ANSWER]
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