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)?
nob n,vhgmc
To answer these questions, we need to determine the sample proportion and calculate the p-value.
1. Sample Proportion:
The sample proportion is calculated by dividing the number of business travelers who use a laptop computer on overnight business trips by the total number of business travelers surveyed.
In this case, the number of business travelers who use a laptop computer is 365, and the total number of business travelers surveyed is 543.
Sample Proportion = Number of business travelers who use a laptop computer / Total number of business travelers surveyed = 365 / 543
Calculating this:
Sample Proportion = 0.672 to 2 decimal places
Therefore, the sample proportion is approximately 0.67.
2. P-value:
To calculate the p-value, we need to conduct a hypothesis test. The null hypothesis assumes that the proportion of business travelers who use a laptop computer on overnight trips is equal to or less than two-thirds. The alternative hypothesis assumes that the proportion is greater than two-thirds.
We can use the binomial distribution to calculate the probability of observing a sample proportion as extreme or more extreme than the observed sample proportion, assuming the null hypothesis is true.
To calculate the p-value, we use a statistical calculator or software, or refer to the Z-table. The Z-value is calculated as (sample proportion - assumed proportion of two-thirds) divided by the standard error.
Using the formula:
Z = (Sample Proportion - Assumed Proportion) / Standard Error
In this case:
Assumed Proportion = 2/3 = 0.667 (approximately)
Standard Error = sqrt((Assumed Proportion * (1 - Assumed Proportion)) / Sample Size)
Calculating this:
Standard Error = sqrt((0.667 * (1 - 0.667)) / 543)
Using a statistical calculator or software, we can find the Z-value associated with the calculated p-value.
Finally, we can use the Z-table to find the corresponding p-value based on the Z-value.
Please note that without the actual Z-value or additional information, it is not possible to provide the specific p-value to 4 decimals.