The nature conservancy has hired you to estimate the population mean of all the lengths of fully grown male killer whales living in captivity. To estimate this population mean, you select a random sample of 14 fully grown male killer whales living in captivity and record the lengths (in m) of each male killer whale. Assume that the population is approximately normally distributed. Based on your sample, follow the steps below to construct a 99% confidence interval for the population mean of all lengths of fully grown male killer whales living in captivity. (If necessary, consult a list of formulas.) (a) Click on "Take Sample" to see the results for your random sample. Take Sample Number of killer whales: 14 Sample mean: 6.697 Sample standard deviation: 1.255 Enter the values of the sample size, the point estimate of the mean, the sample standard deviation, and the critical value you need for your 99% confidence interval. (Choose the correct critical value from the table of critical values provided.) When you are done, select "Compute". Sample size: Point estimate: Sample standard deviation: Critical value: Standard error: Margin of error: 99% confidence interval: Confidence level | Critical value 99% | t0.005 = 3.012 95% | t0.025 = 2.160 90% | t0.050 = 1.771 (b) Based on your sample, enter the lower and upper limits to graph the 99% confidence interval for the population mean of all the lengths of fully grown male killer whales living in captivity.
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- Sample size (\( n \)): 14 - Sample mean (\( \bar{x} \)): 6.697 - Sample standard deviation (\( s \)): 1.255 - Critical value for 99% confidence (\( t_{0.005} \)): 3.012 Show more…
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Section 2. Assume again that you are a wildlife biologist studying the 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. Question 1. What is the point estimate of the population mean? Show your work. (10%) Question 2. Find the margin of error to calculate the 95% confidence interval of the population mean. Show your work. (10%) Question 3. Find the 95% confidence interval of the population mean. Show your work. (10%) Question 4. Interpret the confidence interval found in Question 3. in words. Show your work. (10%)
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Section 1. Suppose that you are a wildlife biologist studying morphological characteristics of 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 x̄. Note this is μ. Question 2. Find the standard deviation of x̄. Note this is the standard error of the mean. Question 3. According to the Central Limit Theorem, what is the shape of the sampling distribution of x̄? What are the values of the center and the spread? Question 4. Using the above distribution, find the probability that the mean carapace length of the sample is less than 96 cm. 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. Question 1. What is the point estimate of the population mean? Show your work. Question 2. Find the margin of error to calculate the 95% confidence interval of the population mean. Show your work. Question 3. Find the 95% confidence interval of the population mean. Show your work. Question 4. Interpret the confidence interval found in Question 3 in words. Show your work.
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