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.
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To determine the confidence interval for total visitors in 2006, we need to use the margin of error provided, which is 7.3%.
The formula for calculating the confidence interval is:
Confidence Interval = Sample Mean +/- (Z * Standard Error)
Since we do not have the sample mean, we will use the total visitor number for 2006, which is 3,281,435, as an estimate of the population mean.
To calculate the standard error, we will apply the formula:
Standard Error = Sample Standard Deviation / Square Root of Sample Size
Here, the sample size is the total visitors for 2006, which is 3,281,435.
As we know that the margin of error is 7.3%, we can write it as a decimal value, which is 0.073.
To find the Z-value for the desired confidence level, we can refer to standard normal distribution tables. Let's assume we want a 95% confidence interval, which corresponds to a Z-value of 1.96.
Now we can plug the values into the formula to get the confidence interval:
Confidence Interval = 3,281,435 +/- (1.96 * (0.073 * 3,281,435) )
Calculating this, we get:
Confidence Interval = 3,281,435 +/- 598,270
Therefore, the confidence interval for total visitors in 2006 is:
(2,683,165, 3,879,705)