Question

B2) To save transportation time, the government improved the roads, they announced that the average time to reach from city A to city B is 35 minutes. A researcher wanted to check the announced result, then has travelled on a random sample of 49 buses on this route from city A to city B and has found that the average time taken is now 32.5 minutes. Assume that the population standard deviation of 8.4 minutes. Using a 5% level of significance, determine whether there is a significant difference in the average time. INB: show all supported graphs) RCI: 10 Marks]

Answer 1

Let the null hypothesis be that there is no significant difference between the two means.

Value of t = xbar -mu / sd/(n)^1/2

= 32.5 -35 / 8.4 /(49)^1/2 = -2.083

Degree of freedom =49-1 =48

Value of t from the table for 5% level of significance with df=48 is given by 2.01 on one end nd -2.01 on other.

Since the vlue of t is less than table value, it falls outside the confidence interval and there is significant difference between the two means.