An airline claims that 65% of its flights depart on time.

Question

An airline claims that 65% of its flights depart on time. A sample of 100 flights was examined and it was determined that 63% left on time. If the goal is to test whether less than 65% of the flights depart on time, what is the value of the critical test statistic at the 5% level of significance?
a.
t = -1.645
b.
t = -1.96
c.
z = -1.645
d.
z = -1.96

Answer 1

Hi Ivan!

Since this question is based on a proportion (the percent of flights that depart on time), not a mean, we use a z-test rather than a t-test. T-tests are used when we are testing means, so answer choices A and B can be eliminated. Next, focus on the wording “less than 65%.” This tells us the test is left-tailed, because we are checking whether the true proportion is below the claimed value.

The hypotheses would be:

H₀: p = 0.65, meaning we start by assuming the airline’s claim is true.

Hₐ: p < 0.65, meaning we are testing if the actual proportion is smaller than what is claimed.

The question asks for the critical value at the 5% significance level, not the test statistic you calculate from the sample data. The critical value is the cutoff that separates the rejection region from the non-rejection region. For a left-tailed z-test with α = 0.05, the critical z-value is −1.645. That’s why the correct answer is choice C.