The National Marine Fisheries Services (NMFS) is part of the National Oceanic an

Question

The National Marine Fisheries Services (NMFS) is part of the National Oceanic and Atmospheric Administration (NOAA). NMFS's programs support the conservation and management of living marine resources. In a study by Hays and Marsh reported in the Canadian Journal of Zoology, 71 loggerhead sea turtles were captured and measured off the coast of Britain. The shell lengths of the turtles are shown in the stem-and-leaf plot below.

1|5 5 6 6 6 7 7 7 8 8 8 8 8 8 8 9 9 9 9 9
|
2|0 0 0 0 0 0 0 0 0 1 1 1 2 2 2 2 2 2 3 4 4
2|5 5 5 6 6 7
|
3|0 0 0 3 4 8
|
4|0 5 9
|
5|1 4
|
6|0 1 1 4
|
7|5 8
|
8|8 8
|
9|0 0 4 6

1) A loggerhead sea turtle is classified as a juvenile if its shell length is less than 40 centimeters. How many of the turtles in the sample were juveniles?

2) Use the sample to make a point estimate of the mean shell length of all juvenile loggerhead sea turtles that drift from their hatching site (in Florida) to the coast of Britain.

3) Find the standard deviation of the sample of juveniles.

4) Use the sample to make an interval estimate of the mean shell length of juvenile loggerhead sea turtles that drift from their hatching site to the coast of Britain.

a) Use a 90% confidence level
b) Use a 95% confidence level
c) Use a 99% confidence level

Explanation / Answer

1) from above number of juveniles =53

2)

point estimate of mean from above values =33.1

3) std deviation =23.118

4)a)std error=std deviation/(n)1/2 =2.763

for 90% CI. t=1.667

hence confidence interval =mean -/+ t*std error =28.522 ; 37.735

b)for 95% CI, t=1.9949

hence confidence interval =mean -/+ t*std error =27.616 ; 38.641

c)for 99% CI, t=2.649

hence confidence interval =mean -/+ t*std error =25.809 ; 40.448

X 15 15 16 16 16 17 17 17 18 18 18 18 18 18 18 19 19 19 19 19 20 20 20 20 20 20 20 20 20 21 21 21 22 22 22 22 22 22 23 24 24 25 25 25 26 26 17 30 30 30 33 34 38 40 45 49 51 54 60 61 61 64 75 78 88 88 90 90 94 96 mean 33.129 std deviation 23.118

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