Question

According to a city's estimate, people on average arrive 1.5 hours early for domestic flights. The population standard deviation is known to be 0.5 hours. A researcher wanted to check if this is true so he took a random sample of 50 people taking domestic flights and found the mean time to be 2.0 hours early. At the 1% significance level, can you conclude that the amount of time people are early for domestic flights is more than what the city claims. Will you reject or not reject the null hypothesis and what is your conclusion in words?

Answer 1

Step 1:

Ho:

Ha:

Step 2: test statistics

n = 50

sample mean = 2

population sd = 0.5

Step 3:

The z-critical value for a right-tailed test, for a significance level of α=0.01

zc = 2.33

As the z stat (7.071) falls in the rejection area, we reject the Null hypothesis.

Hence we have suffucient evidence to believe that the amount of time people are earlu for domestic flights is more than what the city claims; i.e. it is more than 1.5 hrs.