Question

One of the authors came across an article (USA Today, 2008) that said that on average Americans have visited 16 states in the United States. In a survey of 50 students in her introductory statistics class, she found the average number of states the students had visited to be 9.48 and the standard deviation to be 7.13. The data were not strongly skewed.​1. Identify the observational unit for this study.a. studentsb. Americansc. number of states2. Identify the variable of interest and whether it is categorical or quantitative.a. number of U.S. states visited, categorialb. number of students, quantitativec. number of students, categoriald. number of U.S. states visited, quantitative3. Regardless of your answer to part (c), state the null and the alternative hypotheses in symbols, to test whether the average number of states all students at the author’s school have visited is different from 16.a. H0: mu = 16, Ha: mu ≠ 16b. H0: mu = 16, Ha: mu > 16c. H0: mu = 16, Ha: mu < 164. Using the 2SD approach to find a 95% confidence interval for the average number of states all students at the author’s school have visited. Round to two decimal places

Answer 1

1. a. Students

2. d. number of U.S. states visited, quantitative

3. a. H o: mu = 16, Ha: mu ≠ 16

4. (7.46,11.50)

Explanation:

1. The researcher is interested in finding out the average number of states in US that the students have visited.

The unit that is being observed to arrive at that conclusion is the Students. The observational unit for this study is a. Students.

2. The variable of interest from the information above is the number of U.S. states visited. The observations recorded for this variable are in numbers which are numeric in nature. This implies that the variable is quantitative in nature.

Therefore, the answe is d. number of U.S. states visited, quantitative

3. To test whether the average number of states all students at the author’s school have visited,

The null hypothesis (H o) is always given as the negation statement/null of what we wish to test.

So, we wish to test that the average is different from 16. Therefore, the null would be that the average is 16.

Answer is a. H o: mu = 16, Ha: mu ≠ 16

4. A 95% confidence interval for the average number of states all students at the author’s school have visited can be calculated using the formula:

x bar + or - 2 √s/n

=9.48 + or - 2 × 7.13/ √50

= (7.46,11.50)

The 95% confidence interval for the average number of states all students at the author’s school have visited is (7.46,11.50). The average falls betw 7.64 and 11.50.