Shell lengths of sea turtles. Refer to the Aquatic Biology (Vol. 9, 2010) study of green sea turtles inhabiting the Grand Cayman South Sound lagoon, Exercise. Timedepth recorders were deployed on 6 of the 76 captured turtles. The time-depth recorders allowed the environmentalists to track the movement of the sea turtles in the lagoon. These 6 turtles had a mean shell length of 52.9 cm with a standard deviation of 6.8 cm.
a. Use the information on the 6 tracked turtles to estimate, with 99% confidence, the true mean shell length of all green sea turtles in the lagoon. Interpret the result.
b. What assumption about the distribution of shell lengths must be true in order for the confidence interval, part a, to be valid? Is this assumption reasonably satisfied? (Use the data saved in the TURTLES file to help you answer this question.)
Shell lengths of sea turtles. Refer to the Aquatic Biology (Vol. 9, 2010) study of green sea turtles inhabiting the Grand Cayman South Sound lagoon, Exercise. The data on curved carapace (shell) length, measured in centimeters, for 76 captured turtles are displayed in the table and saved in the TURTLES file. Environmentalists want to estimate the true mean shell length of all green sea turtles in the lagoon.
33.96 | 30.37 | 32.57 | 31.50 | 36.46 | 35.54 | 36.16 | 35.32 | 35.99 | |||
39.55 | 44.33 | 42.73 | 42.15 | 42.43 | 49.96 | 46.04 | 48.76 | 47.78 | |||
45.81 | 49.05 | 49.65 | 49.71 | 54.29 | 52.01 | 51.15 | 54.42 | 52.62 | |||
53.27 | 54.07 | 50.40 | 53.69 | 51.30 | 54.29 | 54.58 | 55.11 | 57.65 | |||
56.35 | 55.68 | 58.40 | 58.06 | 57.79 | 66.98 | 57.03 | 57.64 | 59.27 | |||
64.79 | 61.96 | 60.08 | 62.34 | 63.84 | 60.24 | 64.91 | 60.35 | 62.63 | |||
63.33 | 63.00 | 64.55 | 60.03 | 64.75 | 60.61 | 69.01 | 65.07 | 65.77 | |||
65.30 | 68.24 | 65.28 | 67.54 | 68.49 | 56.54 | 65.67 | 70.26 | 70.94 | |||
70.52 | 72.01 | 74.34 | 81.63 |
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a. Define the parameter of interest to the environmentalists.
b. Use the data in the TURTLES file to find a point estimate of the target parameter.
c. Compute a 95% confidence interval for the target parameter. Interpret the result.
d. Suppose a biologist claims that the mean shell length of all green sea turtles in the lagoon is 60 cm. Make an inference about the validity of this claim.
Shell lengths of sea turtles. Aquatic Biology (Vol. 9, 2010) reported on a study of green sea turtles inhabiting the Grand Cayman South Sound lagoon. The data on curved carapace (shell) length (in centimeters) for 76 captured turtles are saved in the TURTLES file. Descriptive statistics for the data are shown on the accompanying MINITAB printout.
Descriptive Statistics: Length | |||||||
Variable | N | Mean | StDev | Variance | Minimum | Maximum | Range |
Length | 76 | 55.47 | 11.34 | 128.57 | 30.37 | 81.63 | 51.26 |
a. Locate the range of the shell lengths on the printout.
b. Locate the variance of the shell lengths on the printout.
c. Locate the standard deviation of the shell lengths on the printout.
d. If the target of your interest is these specific 76 captured turtles, what symbols would you use to represent the variance and standard deviation?
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