Question

In Phoenix, a Rideshare company believes that 50% of all rides originate at the Sky Harbor International Airport. The company decides to sample 30 rides during a particular day. Required: Test the conditions necessary to apply the central limit theorem. Are they satisfied? What is the standard error of the sampling distribution of sample proportions?

Answer 1

The conditions necessary to apply the central limit theorem should be tested, and the standard error of the sampling distribution of sample proportions can be calculated using a formula.

Step-by-step explanation:

To test the conditions necessary to apply the central limit theorem, we need to check if two conditions are satisfied:

1. The sample size should be large enough, typically greater than or equal to 30. In this case, the sample size is 30, so this condition is satisfied.
2. The data should be collected randomly from the population of interest. If the rides were randomly sampled from all the rides in Phoenix, then this condition is also satisfied.

The standard error of the sampling distribution of sample proportions can be calculated using the formula:

Standard Error of Sample Proportions = sqrt((p * q) / n)

where p is the estimated proportion, q is 1 - p, and n is the sample size.