Question

Alamo Rent-A-Car executives believe that Alamo accounts for about 50% of all Cadillacs which are rented. To test this belief a researcher randomly identifies 20 major airports with on-site rental car lots. Observers are sent to each location and instructed to record the number of Rental Company Cadillacs observed in a four-hour period. About 500 are observed, and 30% are observed being returned to Alamo Rent-A-Car. Does he conclude that Alamo accounts for about 50% of all Cadillacs which are rented? (using 95% level of confidence)

Show all work please

Answer 1

Let p denote the proportion of Alamo Rent-A-Car among all Cadillacs.

To test: Vs  

The test statistic is given by,

where, p_obs = 0.30 (Sample proportion) p₀ = 0.50 (Expected / claimed proportion) and n = 500 (sample size)

Substituting the values,

= -8.94

Since, it is a one tailed test, the critical region for our test is Z < Z_crit

Comparing the test statistic value with the critical value from normal tables for ,

Looking for the area , for a left tailed test,

We find that -8.94 < -1.645, and hence, the test statistic value falls in the rejection region. We do not have sufficient evidence to support the claim of the Alamo Rent-A-Car executives. We reject H₀ at 5% level of significance.

We may conclude that based on the given conclusion the researcher cannot conclude that Alamo accounts for about 50% of all Cadillacs which are rented.Based on the sample, the proportion of all Cadillacs that  Alamo accounts for is less than 50%.