Question

In an effort to reduce boarding time, an airline tries a new method of boarding its planes. Historically, only 37% of passengers were satisfied with the boarding process. A random sample of passengers using the new boarding process found that 48% said they were satisfied with the new boarding process.

(a) What are the hypotheses necessary to determine if there is convincing evidence that this new boarding process resulted in improved passenger satisfaction?

- H0:p = 0.37 ; Ha:p < 0.37

- H0:p = 0.48 ; Ha:p > 0.48

- H0:p = 0.48 ; Ha:p < 0.48

- H0:p = 0.37 ; Ha:p > 0.37

(b) The airline decided to test the hypotheses at the 0.05 level of significance. They made the correct decision based on the p-value but this resulted in a type I error. Complete the following three statements.

(1) The airline ____ the null hypothesis.

(2) The airline found there _____(enough or not enough) evidence to conclude the new boarding process improved passenger satisfaction

(3) Actually, the new boarding process ______(improved or did not improve) passenger satisfaction.

Answer 1

(A) Researcher wanted to test whether the new boarding process has improved passenger satisfaction

True proportion given is p = 0.37

Improved passenger satisfaction means increased proportion, i.e. right tailed

so, we can assume that the null hypothesis that the proportion is equal to 0.37

and alternate hypothesis is that the proportion is greater or more than 0.37

Option D is correct

(B) Type I error is defined as the rejection of a true null hypothesis, i.e. rejecting the null hypothesis when it is true. This means in this hypothesis, the p value must be greater than the significance level 0.05.

(1) The airline rejected the null hypothesis

(2) The airline found that there is enough evidence to conclude that the new boarding process improved passenger satisfaction.

(3) Actually, the new boarding process didn’t improved passenger satisfaction.