An airline promotion to business travelers is based on the assumption that no more than two-thirds of business travelers use a laptop computer on overnight business trips.
1. What is the sample proportion from an American Express-sponsored survey that found 365 of 543 business travelers use a laptop computer on overnight business trips (to 2 decimals)?
2. What is the p-value (to 4 decimals)?
To answer the questions, we need to calculate the sample proportion and the p-value. Let's go step-by-step.
1. Sample Proportion:
The sample proportion is the number of business travelers who use a laptop computer on overnight business trips divided by the total number of business travelers in the survey.
Given:
Number of business travelers using a laptop computer = 365
Total number of business travelers in the survey = 543
Sample Proportion = Number of business travelers using a laptop computer / Total number of business travelers in the survey
Sample Proportion = 365 / 543
Calculating this division yields: Sample Proportion ≈ 0.6721 (rounded to 2 decimals)
Therefore, the sample proportion of business travelers using a laptop computer on overnight business trips is approximately 0.6721.
2. P-Value:
To calculate the p-value, we need to perform a hypothesis test using the sample proportion and the assumption provided.
Assumption: The assumption states that no more than two-thirds of business travelers use a laptop computer on overnight business trips.
Null Hypothesis (H0): The true proportion of business travelers using a laptop computer on overnight business trips is equal to or less than two-thirds.
Alternative Hypothesis (Ha): The true proportion of business travelers using a laptop computer on overnight business trips is greater than two-thirds.
We can use a one-sample proportion z-test to test this hypothesis. However, to calculate the p-value, we need additional information, such as the population proportion. Without that information, we cannot calculate the p-value.
Please note that the p-value would be calculated by comparing the sample proportion to the assumed population proportion. If we had the population proportion, we would determine the test statistic (z-statistic) corresponding to the sample proportion and calculate the p-value based on the test statistic.
Without the necessary information, it is not possible to provide the p-value in this scenario.