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b. Calculate a 95% confidence interval for the mean number of young per litter for all Garter Snakes bred in captivity. (to 3 decimal places) Remember: Art of Stat does NOT do confidence intervals for when the population standard deviation is known. You must use a TI Calculator with Z-interval OR the book calculator in section 8.2 <με c. How can we interpret the confidence interval from b. (Hint: there are actually two possible correct answers here.)

b. Calculate a 95% confidence interval for the mean number of young per litter for all Garter Snakes bred in captivity. (to 3 decimal places) Remember: Art of Stat does NOT do confidence intervals for when the population standard deviation is known. You must use a TI Calculator with Z-interval OR the book calculator in section 8.2 <με c. How can we interpret the confidence interval from b. (Hint: there are actually two possible correct answers here.)

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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### Sources of Variation in Estimating Litter Characteristics of the Garter Snake, *Thamnophis elegans* By Daniel R. Farr and Patrick T. Gregory, this study was published in the **Journal of Herpetology** (Vol. 25, No. 3, Sep. 1991, pp. 261-268). In this study, 31 random female snakes were captured and bred. The mean litter size observed was 7.87 young. Assume that the population standard deviation of litter size in Garter Snakes is 2.0. **Question:** a. Is it likely that the sample mean found above is exactly equal to the mean litter size of all Garter Snakes bred in captivity? - Options: - ○ yes - ● no The correct answer is "no." **Explanation:** - Options: - ○ Because we did the calculations correctly - ● Because we only had 31 snakes and we are probably off the true mean - ○ Because these are snakes in captivity - ○ Because litter size is a discrete variable - ○ Because we were told the population standard deviation - ○ Because of sampling error The correct reason is "Because we only had 31 snakes and we are probably off the true mean." This indicates that the sample size is not sufficient to guarantee that the sample mean exactly matches the population mean, suggesting potential variation from the true mean.
Transcribed Image Text:### Sources of Variation in Estimating Litter Characteristics of the Garter Snake, *Thamnophis elegans* By Daniel R. Farr and Patrick T. Gregory, this study was published in the **Journal of Herpetology** (Vol. 25, No. 3, Sep. 1991, pp. 261-268). In this study, 31 random female snakes were captured and bred. The mean litter size observed was 7.87 young. Assume that the population standard deviation of litter size in Garter Snakes is 2.0. **Question:** a. Is it likely that the sample mean found above is exactly equal to the mean litter size of all Garter Snakes bred in captivity? - Options: - ○ yes - ● no The correct answer is "no." **Explanation:** - Options: - ○ Because we did the calculations correctly - ● Because we only had 31 snakes and we are probably off the true mean - ○ Because these are snakes in captivity - ○ Because litter size is a discrete variable - ○ Because we were told the population standard deviation - ○ Because of sampling error The correct reason is "Because we only had 31 snakes and we are probably off the true mean." This indicates that the sample size is not sufficient to guarantee that the sample mean exactly matches the population mean, suggesting potential variation from the true mean.
**a. Why is your estimate probably off the true mean?** - ○ Because these are snakes in captivity - ○ Because litter size is a discrete variable - ○ Because we were told the population standard deviation - ○ Because of sampling error - ✔ **b. Calculate a 95% confidence interval for the mean number of young per litter for all Garter Snakes bred in captivity. (to 3 decimal places)** Remember: **Art of Stat does NOT do confidence intervals for when the population standard deviation is known.** You must use a TI Calculator with Z-interval OR the book calculator in section 8.2. \[\_ \leq \mu \leq \_\] **c. How can we interpret the confidence interval from b. (Hint: there are actually two possible correct answers here.)** - ○ We can be 95% confident that these 31 garter snakes have a mean litter size in this interval. - ● If 31 garter snakes bred in captivity were repeatedly sampled and confidence intervals calculated, approximately 95% of these intervals would contain the true mean litter size for all such snakes.
Transcribed Image Text:**a. Why is your estimate probably off the true mean?** - ○ Because these are snakes in captivity - ○ Because litter size is a discrete variable - ○ Because we were told the population standard deviation - ○ Because of sampling error - ✔ **b. Calculate a 95% confidence interval for the mean number of young per litter for all Garter Snakes bred in captivity. (to 3 decimal places)** Remember: **Art of Stat does NOT do confidence intervals for when the population standard deviation is known.** You must use a TI Calculator with Z-interval OR the book calculator in section 8.2. \[\_ \leq \mu \leq \_\] **c. How can we interpret the confidence interval from b. (Hint: there are actually two possible correct answers here.)** - ○ We can be 95% confident that these 31 garter snakes have a mean litter size in this interval. - ● If 31 garter snakes bred in captivity were repeatedly sampled and confidence intervals calculated, approximately 95% of these intervals would contain the true mean litter size for all such snakes.
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