Question

Data from 2011 shows that 25% of all flights from IAH departed late. An analyst took a simple random sample of 400 flights from IAH in 2019 and found that 92 flights departed late. Has the proportion of flights from IAH that departed late decreased from 2011 to 2019? Conduct a hypotheses testing with 5% significance level. State the null and alternative hypotheses, test statistics, p-value, and state the conclusion.

Answer 1

Step 1:

Ho: p = 0.25

Ha: p < 0.25

Null hypothesis states that the proportion of flights that departed late in year 2011 are 0.25

Alternative hypothesis states that the proportion of flights that departed late in year 2011  are less than 0.25

Step 2: Test statistics

x = 92

n = 400

z = - 0.92

p value

P(z < 0.92) = 1- P (z < 0.92) = 1- 0.8212 = 0.1788

As the p value (0.1788) is greater than (0.05), we fail to reject the Null hypothesis.

Hence we do not have sufficient evidence to believe that the proportion of flights that departed late in year 2011  are less than 0.25