A bus company is doing market research about its customers and changes to its routes. The company sends out a survey to 1500 persons who are existing or potential passengers and receives back 864 responses. One survey question asks "Do you have a mobility disability?", 39 people reply that they have such a disability. The company needs to provide extra special seating on buses if more than 4% of its passengers have a mobility disability. Use a hypothesis test at a 5% level of significance to help the company make a decision about its bus fleet.

What is the null hypothesis??

The null hypothesis is H0: π=0.04
The alternative is H1: π > 0.04
Check the conditions for normality and find the test statistic(n=864)
nπ0=864(0.04)=34.56>5 n(1−π0)=864(1-0.04)=829.44 > 5
The test statistic is:
Z= 0.75
From Table E.2, the probability of a Z value above 0.75 is 0.7734
Since 0.7734> 0.05 , we will not reject the null hypothesis
conclude that there is insufficient evidence at the 5% level of significance that more than 4% of its passengers have a mobility disability.