In a survey of 40 students in an introductory statistics class, a professor asks how many states in the United States each student has visited. Using the data from the professor's sample, a 99% confidence interval for the average number of states all students at the professor's school have visited is found to be (6.78, 12.18). Determine whether each of the following statements is valid or invalid. You may assume that the sample is representative of all students at the professor's school. (a) We are 99% confident that the average number of states visited by the 40 students the professor surveyed is between 6.78 and 12.18. Valid Invalid (b) Based on the 99% confidence interval, there is evidence that the average number of states visited by all students at the professor's school is different from 16. Valid Invalid (c) We are 99% confident that the average number of states visited by all students at the professor's school is between 6.78 and 12.18. Valid Invalid (d) Based on the 99% confidence interval, there is evidence that the average number of states visited by all students at the professor's school is 16. Valid Invalid (e) About 99% of the students at the professor's school have visited between 6.78 and 12.18 states. Valid Invalid (f) If we want to be less than 99% confident, we should take a smaller sample of students. Valid Invalid
In a survey of 40 students in an introductory statistics class, a professor asks how many states in the United States each student has visited. Using the data from the professor's sample, a 99% confidence interval for the average number of states all students at the professor's school have visited is found to be (6.78, 12.18). Determine whether each of the following statements is valid or invalid. You may assume that the sample is representative of all students at the professor's school.
(a) We are 99% confident that the average number of states visited by the 40 students the professor surveyed is between 6.78 and 12.18.
- Valid
- Invalid
(b) Based on the 99% confidence interval, there is evidence that the average number of states visited by all students at the professor's school is different from 16.
- Valid
- Invalid
(c) We are 99% confident that the average number of states visited by all students at the professor's school is between 6.78 and 12.18.
- Valid
- Invalid
(d) Based on the 99% confidence interval, there is evidence that the average number of states visited by all students at the professor's school is 16.
- Valid
- Invalid
(e) About 99% of the students at the professor's school have visited between 6.78 and 12.18 states.
- Valid
- Invalid
(f) If we want to be less than 99% confident, we should take a smaller sample of students.
- Valid
- Invalid
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