Visitor Numbers
Total visitors: 2004. 2005. 2006
3,135,727. 3,164,906. 3,281,435
Total visitor days: 2004. 2005. 2006
7,453,465. 7,518,997. 7,784,044
Total visitors have increased by 4.6% and total visitor days by 4.4% in this period. Group tour visitors have increased slightly from 11.6% to 12.6% of the total. These figures are not absolutes as the margin of error for total visitors is 7.5% and for total visitor days, 7.3%.
1.) Determine the confidence interval for total visitors in 2006.
To determine the confidence interval for total visitors in 2006, we need to consider the margin of error and the percentage increase in total visitors.
Given:
- Total visitors in 2006: 3,281,435
- Percentage increase in total visitors: 4.6%
- Margin of error for total visitors: 7.5%
Step 1: Calculate the margin of error.
The margin of error is calculated by multiplying the total visitors in 2006 by the margin of error percentage:
Margin of error = (Margin of error percentage / 100) * Total visitors in 2006
Margin of error = (7.5 / 100) * 3,281,435 = 246,107.63
Step 2: Calculate the lower and upper bounds of the confidence interval.
Lower bound = Total visitors in 2006 - Margin of error
Lower bound = 3,281,435 - 246,107.63 = 3,035,327.37
Upper bound = Total visitors in 2006 + Margin of error
Upper bound = 3,281,435 + 246,107.63 = 3,527,542.63
Therefore, the confidence interval for total visitors in 2006 is (3,035,327.37, 3,527,542.63).
To determine the confidence interval for total visitors in 2006, we need to use the margin of error and the percent change given.
1. Calculate the percent change in total visitors from 2004 to 2006:
Percent Change = (Total Visitors in 2006 - Total Visitors in 2004) / Total Visitors in 2004 * 100
Percent Change = (3,281,435 - 3,135,727) / 3,135,727 * 100
Percent Change = 145,708 / 3,135,727 * 100
Percent Change ≈ 4.64%
2. Calculate the margin of error for total visitors:
Margin of Error = Percent Change * Margin of Error for total visitors
Margin of Error = 4.64% * 7.5%
Margin of Error ≈ 0.348%
3. Calculate the confidence interval:
Lower Bound = Total Visitors in 2006 - Margin of Error
Lower Bound = 3,281,435 - 0.348% * 3,281,435
Lower Bound ≈ 3,270,361
Upper Bound = Total Visitors in 2006 + Margin of Error
Upper Bound = 3,281,435 + 0.348% * 3,281,435
Upper Bound ≈ 3,292,509
The confidence interval for total visitors in 2006 is approximately 3,270,361 to 3,292,509.