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    Shell Lengths of Loggerhead Sea Turtles

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    Shell Lengths of Loggerhead Sea Turtles

    The National Marine Fisheries Services is part of the National Oceanic and Atmospheric Administration. NMFS's programs support the conservation and management of living marine resources. There are six species of sea turtles in the United States and all are protected as endangered or threatened species. Rarely does a hatchling sea turtle live to maturity. In fact, it is believed that only 1 in 10,000 hatchlings lives long enough to reproduce. In a study by Hays and Marsh reported in the Canadian Journal of Zoology (75: 40 - 46, 1997), 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.

    Part of the purpose of the study was to estimate the growth rate of juvenile turtles. The turtles were hatched off the coast of Florida and their drifting time in the Atlantic Ocean was estimated to be between 1.8 and 3.75 years. From this and the fact that a typical hatchling has a shell length of 4.5 centimeters, Hays and Marsh estimated that juvenile loggerhead sea turtles grow at a rate of between 4.3 and 8.9 centimeters per year.

    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 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.
    5. How would your results have differed if you had used all the turtles in the sample instead of just the juvenile turtles? Explain your reasoning.
    6. Complete the following table.
    Shell length
    Juvenile Length at Length at Shell
    Turtles Hatching Capture Growth

    Minimum 4.5 cm 15 cm ?? cm

    Maximum 4.5 cm 40 cm ?? cm

    Use the table to estimate the rate of growth for juvenile loggerhead sea turtles under the following assumptions.
    (a) Drift time = 1.8 years, minimum shell growth
    (b) Drift time = 3.75 years, maximum shell growth

    Data
    1 - 5 5 6 6 6 7 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
    3 - 8 Key: 1 / 5 = 15 cm
    4 - 0
    4 - 5 9
    5 - 1 4
    5
    6 - 0 1 1 4
    6
    7
    7 - 5 8
    8
    8 - 8 8
    9 - 0 0
    9 - 6
    10 - 4

    © BrainMass Inc. brainmass.com October 10, 2019, 5:51 am ad1c9bdddf
    https://brainmass.com/statistics/confidence-interval/shell-lengths-loggerhead-sea-turtles-519877

    Solution Preview

    1. For the length that is less than 40 centimeters, the stem is 1, 2 and 3. Therefore, there are 54 turtles that were juveniles.
    2. A point estimate:
    Mean=(15+15+16+16+16+17+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+27+
    30+30+30+33+34+38)/54=21.51852
    Therefore, a point estimate of the mean shell length is 21.51852 cm.
    3. Standard ...

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