Travelers Pay Taxes For Flying Car Rentals And Hotels

Travelers Pay Taxes For Flying Car Rentals And Hotels

Travelers pay taxes for flying, car rentals, and hotels. The following data represent the total travel tax for a 3-day business trip in either randomly selected cities: 67.81, 78.69, 68.99, 84.36, 80.24, 86.14, 101.27, 99.29.

(a) Determine a point estimate for the population mean travel tax.

(b) Construct and interpret a 95% confidence interval to estimate the mean tax paid for a 3-day business trip.

Paper For Above instruction

Travel and tourism are significant sectors in the global economy, with travelers often incurring various expenses such as transportation, accommodation, and service taxes. Understanding the average tax burden on travelers and accurately estimating this mean value through statistical methods like confidence intervals can provide valuable insights for policymakers, businesses, and travelers themselves. This paper discusses the process of estimating the population mean of total travel taxes paid during a three-day business trip, based on given sample data, and constructing a corresponding confidence interval to understand the variability and reliability of this estimate.

Introduction

The analysis of travel-related expenses, specifically taxes, is crucial for understanding the economic impact of travel. Since the cost can vary significantly across different locations and services, statistical analysis helps in providing an average estimate and an understanding of the uncertainty associated with that estimate. The data in question comprises eight sample observations of total travel taxes paid in various cities, and the goal is to estimate the average tax and construct a 95% confidence interval around this estimate.

Part A: Point Estimate of the Population Mean

The point estimate of the population mean is calculated as the sample mean, which summarizes the average tax paid based on the observed data. The sample data provided are:

  • 67.81
  • 78.69
  • 68.99
  • 84.36
  • 80.24
  • 86.14
  • 101.27
  • 99.29

Calculating the sample mean involves summing all observations and dividing by the number of observations (n = 8):

Sample Mean (x̄) = (67.81 + 78.69 + 68.99 + 84.36 + 80.24 + 86.14 + 101.27 + 99.29) / 8

= (666.99) / 8 ≈ 83.37

Therefore, the point estimate for the population mean travel tax is approximately $83.37.

Part B: Constructing a 95% Confidence Interval

To construct a 95% confidence interval for the population mean, the following steps are taken:

  1. Calculate the sample standard deviation (s).
  2. Determine the appropriate t-value for the 95% confidence level with n-1 degrees of freedom (df = 7).
  3. Compute the margin of error (ME).
  4. Construct the confidence interval as (x̄ - ME, x̄ + ME).

Calculating the sample standard deviation (s):

First, find each deviation from the mean, square it, sum all squared deviations, and divide by (n - 1) to get the variance, then take the square root for s.

Deviations squared:

  • (67.81 - 83.37)² ≈ 243.47
  • (78.69 - 83.37)² ≈ 22.50
  • (68.99 - 83.37)² ≈ 205.87
  • (84.36 - 83.37)² ≈ 0.99
  • (80.24 - 83.37)² ≈ 9.95
  • (86.14 - 83.37)² ≈ 7.99
  • (101.27 - 83.37)² ≈ 317.63
  • (99.29 - 83.37)² ≈ 253.44

Sum of squared deviations ≈ 243.47 + 22.50 + 205.87 + 0.99 + 9.95 + 7.99 + 317.63 + 253.44 ≈ 1061.84

Variance (s²) ≈ 1061.84 / (8 - 1) ≈ 1061.84 / 7 ≈ 151.69

Standard deviation (s) ≈ √151.69 ≈ 12.32

Determining the t-value:

For a 95% confidence level and df = 7, the t-value from t-distribution tables is approximately 2.365.

Calculating the margin of error (ME):

ME = t × (s / √n) = 2.365 × (12.32 / √8) ≈ 2.365 × (12.32 / 2.828) ≈ 2.365 × 4.355 ≈ 10.30

Constructing the confidence interval:

Lower bound = 83.37 - 10.30 ≈ 73.07

Upper bound = 83.37 + 10.30 ≈ 93.67

Thus, the 95% confidence interval for the mean travel tax is approximately ($73.07, $93.67).

Interpretation of the Confidence Interval

The calculated 95% confidence interval indicates that there is a 95% probability that the true average travel tax for a three-day business trip falls between approximately $73.07 and $93.67. This interval reflects the inherent variability in traveling expenses across different cities and provides a range estimate within which the actual mean is likely to lie with high confidence.

Conclusion

In summary, the point estimate for the average travel tax paid during a three-day business trip based on the sample is approximately $83.37. The corresponding 95% confidence interval, from about $73.07 to $93.67, offers a statistical range where the true population mean is likely to be found. Such analyses are vital for informed decision-making in travel planning, budgeting, and policy formulation related to tourism taxes.

References

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