Question

An SRS of 170 flights of a large airline (call this airline 1) showed that 140 were on time. An SRS of 170 flights of another large airline (call this airline 2) showed that 152 were on time. Let p1 and p2 be the proportion of all flights that are on time for these two respective airlines. Is airline 2 more reliable? In other words, does airline 1 have a lower on-time rate compared to airline 2? Carry out an appropriate test using a significance level of 0.01.

(a) What are the null and alternative hypotheses?
H0: ["p" OR "μ" OR "p1 - p2" OR "μ1 - μ2" OR "μd"] ["<" OR "≠" OR ">" OR "="] [0.0 OR -0.0706]
HA: ["p" OR "μ" OR "p1 - p2" OR "μ1 - μ2" OR "μd"] ["=" OR "≤" OR "≥" OR "<" OR "≠" OR ">"] [0.0 OR -0.0706]

Answer 1

This is a test of proportions to compare the on-time rates of two airlines. The null hypothesis is that both airlines have the same on-time rate, while the alternative hypothesis is that airline 1 has a lower on-time rate compared to airline 2. By carrying out a two-sample z-test and comparing the p-value to the significance level, you can conclude whether airline 2 is more reliable.

Step-by-step explanation:

This is a test of proportions. The random variable is the proportion of on-time flights for each airline.

The null and alternative hypotheses are:

• H0: p1 = p2 (Both airlines have the same on-time rate)
• HA: p1 < p2 (Airline 1 has a lower on-time rate compared to airline 2)

To carry out the hypothesis test, you can use the two-sample z-test.

The p-value can be calculated using a statistical software or a z-table. If the p-value is less than the significance level of 0.01, you can reject the null hypothesis and conclude that airline 1 has a lower on-time rate compared to airline 2, making airline 2 more reliable in terms of on-time performance.