Tuatara are rare, medium-sized reptiles found only in New Zealand.The length of each tuatara in a random sample of 10 female tuatara is measured giving an average length of 48.5cm with a standard deviation of 2.9cm. This information is to be used to calculate a 95% confidence interval for the true mean length of female tuatara.Use the drop-down menus to identify if the following conditions for constructing this confidence interval are satisfied or not.The sample is representative of the population.AnswerThe sampling distribution of the sample mean normal.
Question
Tuatara are rare, medium-sized reptiles found only in New Zealand.The length of each tuatara in a random sample of 10 female tuatara is measured giving an average length of 48.5cm with a standard deviation of 2.9cm. This information is to be used to calculate a 95% confidence interval for the true mean length of female tuatara.Use the drop-down menus to identify if the following conditions for constructing this confidence interval are satisfied or not.The sample is representative of the population.AnswerThe sampling distribution of the sample mean normal.
Solution
- The sample is representative of the population.
Answer: This condition is generally assumed to be satisfied in statistical problems unless there is information given that suggests otherwise. In this case, there is no information suggesting that the sample is not representative of the population. Therefore, we can say this condition is satisfied.
- The sampling distribution of the sample mean is normal.
Answer: The Central Limit Theorem states that if the sample size is large enough (usually n > 30), the sampling distribution of the sample mean is approximately normal, regardless of the shape of the population distribution. However, in this case, the sample size is only 10, which is less than 30. Therefore, we cannot automatically assume that the sampling distribution is normal based on the Central Limit Theorem. However, the problem states that the lengths of the tuatara are normally distributed. When the population is normally distributed, the sampling distribution of the sample mean is also normal, regardless of the sample size. Therefore, we can say this condition is satisfied.
Similar Questions
Tuatara are rare, medium-sized reptiles found only in New Zealand. Assume female lengths are normally distributed.The length of each tuatara in a sample of 10 female tuatara is measured giving an average length of 48.5cm with a standard deviation of 2.9cm.Suppose we repeatedly took random samples of 10 female tuatara. What percentage of these samples would we expect to have a sample mean weight that is less than 50.34cm?(You should use the empirical rules to estimate this percentage.)Select one:a.2.5%b.100%c.95%d.97.5%
Giant weta, native to New Zealand, are among the largest insects in the world. Their body lengths have a mean of 90 mm and a standard deviation of 3.6 mm.The lengths of a random sample of 36 giant weta is measured. Which of the following is the most accurate description of the distribution of the sample mean length?Select one:a.It is normal with a mean of 90mm and a standard error of 3.6mm.b.It has a mean of 90mm and a standard error of 0.6mm.c.It has a mean of 90mm and a standard error of 3.6mm.d.It is normal with a mean of 90mm and a standard error of 0.6mm.
he heights of women in New Zealand are normally distributed, with a mean of 165 centimetres and a standard deviation of 10 centimetres. A random sample of five women is selected. What is the probability that the sample mean is greater than 162 centimetres?
Powelliphanta, New Zealand’s native snails, are among the largest snails in the world. Their weight has a normal distribution with mean of 85 grams and standard deviation of 6.4 grams. Suppose we repeatedly took random samples of 10 of these snails.The percentage of samples that have a sample mean weight less than 81grams is closest to:
Giant weta, native to New Zealand, are among the largest insects in the world. Their weight is normally distributed with mean of 25 g and standard deviation of 1.9 grams.A random sample of 10 giant weta is obtained. What is the standard error of the sample mean?(Give the answer to 3 decimal places.)
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.