The following is taken from a State of the Park Report for Banff National Park.

Visitors Numbers
Total Visitors: 2004= 3,135,727. 2005=3,164,906. 2006=3,281,435
Total visitor days: 2004= 7,453,465. 2005= 7,518,997. 2006= 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.

Explanation:

Total visitors for 2006 = 3,281,435

Margin of error = 7.5% of 3,281,435

= 0.075 * 3,281,435

= 246, 107.625

Confidence interval:

Lower bound = Total visitors for 2006 - margin of error

= 3,281,435 - 246, 107.625

= 3035327. 375

= 3035328 ( round up)

Upper bound = Total visitors for 2006 + margin of error

= 3,281,435 + 246, 107.625

= 3527542.625

= 3527543 ( round up)

To determine the confidence interval for total visitors in 2006, we can use the margin of error provided and the formula for calculating a confidence interval.

The formula for a confidence interval is:

Confidence Interval = Sample Statistic +/- Margin of Error

The margin of error is calculated by multiplying the critical value (z-score) with the standard deviation of the sample.

In this case, we are given the margin of error as 7.5% and the sample statistic as the total visitors in 2006, which is 3,281,435.

To compute the confidence interval, we need to find the critical z-score. The z-score corresponds to the desired level of confidence. Since the State of the Park Report does not mention the confidence level, let's assume a 95% confidence level.

For a 95% confidence level, the critical z-score is approximately 1.96.

Now, we can calculate the confidence interval using the formula:

Confidence Interval = Sample Statistic +/- Margin of Error

Confidence Interval = 3,281,435 +/- (1.96 * 7.5% * 3,281,435)

Confidence Interval = 3,281,435 +/- (1.96 * 0.075 * 3,281,435)

Confidence Interval = 3,281,435 +/- 607,452

The confidence interval for the total visitors in 2006 is approximately (2,673,983, 3,888,887).

Please note that this calculation assumes a 95% confidence level. If a different confidence level is desired, the critical z-score would need to be adjusted accordingly.

To determine the confidence interval for total visitors in 2006, we need to calculate the margin of error first. The margin of error is based on the reported margin of error for total visitors, which is stated as 7.5%.

Step 1: Calculate the margin of error:
Margin of Error = 7.5% of the reported total visitors in 2006
= 7.5% of 3,281,435
≈ 246,106

Step 2: Calculate the lower and upper bounds of the confidence interval:
Lower Bound = Reported total visitors in 2006 - Margin of Error
= 3,281,435 - 246,106
≈ 3,035,329

Upper Bound = Reported total visitors in 2006 + Margin of Error
= 3,281,435 + 246,106
≈ 3,527,541

Therefore, the confidence interval for total visitors in 2006 is approximately between 3,035,329 and 3,527,541 visitors.