The housing crisis and lack of spending on roads and railways is leading to longer commutes for workers.

The number of workers who commute daily for more than an hour has increased by a third in five years. A survey was conducted in a city on the number of reports claimed by the commuter who spends more than one hour travelling from home to work. Five commuters per day are surveyed and the daily number of reports made in the past 150 days is recorded in the following table. Assuming the survey with the number of reports made is evaluated by using a binomial distribution with n = 5 and p = 0.6.

Number of Reports Reports 0 0 1 5 2 24 3 32 4 75 5 14

a. Determine the expected values for each number of reports. (Hint: Combine the expected value which is less than 5.)

b. Identify whether the assumption in the question is true or not. Justify your answer at 1% significance level.