MATH 201 Statistics for Environmental Professionals ● Worksheet 3 (2)

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MATH 201 Statistics for Environmental Professionals ● Worksheet 3 Name: Mandi Harp sea turtles. Assume that the mean straight carapace length of all adult female loggerhead sea turtles is 98 cm and the standard deviation is 12 cm. You did not know this fact and measured the straight carapace length of randomly caught 36 female loggerhead sea turtles. Refer to the textbook 7.1. Question 1. Find the mean of the sampling distribution of 𝑥 . Note this is 𝜇 𝑥 . (10 pts.) Question 2. Find the standard error of the mean. (10 pts.)

Question 3. According to the Central Limit Theorem, what is the shape of the sampling distribution of 𝑥 ? What are the values of the center and the spread? (10 pts.) Question 4. Using the above distribution, find the probability that the mean carapace length of the Sample is less than 96 cm. (10 pts.)

Section 2. Assume again that you are a wildlife biologist studying morphological characteristics of Sea turtles. Now you would like to estimate the population mean of straight carapace length of adult female loggerhead sea turtles. Based on the randomly caught 36 female loggerhead sea turtles, the sample mean is 99 cm and the sample standard deviation is 16 cm. Refer to your textbook 8.2. Question 1. What is the point estimate of the population mean? Show your work.(10 pts.)

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Question 2. Find the margin of error to calculate the 95% confidence interval of the population mean. Show your work. (10 pts.) Question 3. Find the 95% confidence interval of the population mean. Show your work. (10 pts.) Question 4. Interpret the confidence interval found in Question 3 in 50-100 words. (10 pts.)

Section 3. The accompanying data file contains measured straight carapace lengths (SCL) of juvenile neritic loggerhead sea turtles. Using the provided Excel worksheet for calculating confidence Intervals, calculate the 95% confidence interval for the population mean of SCL for juvenile neritic loggerhead sea turtles. Report the lower limit and upper limit of the interval and attach the output to this report. (20 pts.)

Lower limit:54.338 Upper limit:66.512 Source: Snover M, Avens L, Hoh AA (2007) Back-calculating length from skeletal growth marks in loggerhead sea Turtles Caretta caretta . Endangered Species Research. 3: 95–104.

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MATH 201 Statistics for Environmental Professionals ● Worksheet 3 (2)

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