In a remote part of the country, a bus line runs between a small town and a larger urban area. They wanted to investigate whether there is a need to increase the number of departures in the evening from the smaller town (and back a little later in the evening of course, there is a cinema and other entertainment in the larger town).

an unbound random sample, without recurrence, was drawn, consisting of = 50 people from the population in the smaller locality which at the time of the survey consisted of = 200 inhabitants. Telephone interviews asked the selected how many times they had traveled with the bus line during the evening in a given reference week (same for everyone) and got the following results:

Number of times you went:0,1,2,3,4

Number of people.:14,18,10,8,0

In your calculations, finality correction should be used.

a) Calculate a 90% confidence interval for the proportion of people in the smaller town who traveled with the bus line at least once during the reference week.

b) Assume that the total length of a 99% confidence interval for the share estimate in a) may not exceed 2 percentage points. How many people do you have to examine at least then? Assume that the number of people in the smaller town who travel by bus is equal to the number who do not travel