Use the following information for the next two questions. According to USA Today
ID: 3331695 • Letter: U
Question
Use the following information for the next two questions.
According to USA Today, 2008, Americans on average have visited 16 states in the United States. In a survey of 50 randomly selected students in an introductory statistics class, the average number of states the students had visited was 9.48 with a standard deviation of 7.13.
What is the variable of interest? What type of variable is this?
Question options:
proportion of students who have visited at least 16 states, categorical
whether or not a student has visited at least 16 states, categorical
average number of states visited, quantitative
number of states visited, quantitative
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A 99% confidence interval for the average number of states visited by all students is found to be (6.78, 12.18). Select all of the following that apply.
Question options:
We are 99% confident the true mean number of states students had visited is between 6.78 and 12.18 states.
We are 99% confident the sample mean number of states these 50 students had visited is between 6.78 and 12.18 states.
There is evidence that the true mean number of states visited by students is less than 16 states.
There is little to no evidence that the true mean number of states visited by students differs from 16 states.
proportion of students who have visited at least 16 states, categorical
whether or not a student has visited at least 16 states, categorical
average number of states visited, quantitative
number of states visited, quantitative
----
A 99% confidence interval for the average number of states visited by all students is found to be (6.78, 12.18). Select all of the following that apply.
Question options:
We are 99% confident the true mean number of states students had visited is between 6.78 and 12.18 states.
We are 99% confident the sample mean number of states these 50 students had visited is between 6.78 and 12.18 states.
There is evidence that the true mean number of states visited by students is less than 16 states.
There is little to no evidence that the true mean number of states visited by students differs from 16 states.
The equation for the theory based Confidence Interval for a single quantitative variable is ± multiplier x Vn p ± multiplier x x ± multiplier x s /nExplanation / Answer
1) Variable of interest is: average number of states visited
type of variable is quantitative i.e we can measure numerically.
2) Given A 99% confidence interval for the average number of states visited by all students is found to be (6.78, 12.18)
Conclusion:
We are 99% confident the true mean number of states students had visited is between 6.78 and 12.18 states.
Null hypotheis: the true mean number of states visited by students is equals to 16 states.
Alternative hypothesis: the true mean number of states visited by students differs from 16 states.
alpha:1%
Conclusion:
99% confident the true mean number of states students had visited is between 6.78 and 12.18 states.
Hence population mean(16) is does not include in the interval . hence we reject the H0.
There is evidence that the true mean number of states visited by students is less than 16 states.