Question

1) An ambulance service located at the edge of town is responsible for servicing a large office building in the downtown area. One of the drivers would like to find the quickest route from the ambulance station to the office building and has identified to candidates: route A and route B b) Choose a level of a. Use a -0.0 5 for this problenm c) To test the hypothesis, the driver travels route A five times and route B six times. The data appear in the Ambulance worksheet of the HW2 data workbook on Moodle. Use Excel to perform the hypothesis test. d) Draw a conclusion and report that in the problem context

Answer 1

Let population 1: Route A

population 2: Route B

a)

Hypotheses are:

$H_{0}:\mu_{1}=\mu_{2}$

$H_{a}:\mu_{1}\neq \mu_{2}$

Following is the output of summary statistics:

Descriptive statistics Route A Route B 6 5.900 4.200 sample standard deviation1.402 800 3.240 count mean sample variance 1.965

b)

Here we have =5.9, si-1.402, =5 T24.2,s2 -1.8, n2 -6 Hypotheses are: Test is two tailed. Level of significance: α-0.05 Since we can assume that variances are equal so degree of freedom of t test will be:

Critical value of t using excel function "=TINV(0.05,9)" is +/- 2.262.

Rejection region:

If t < -2.262 or t > 2.262, reject H0

c)

Following is the two tailed t test:

Hypothesis Test: Independent Groups (t-test, pooled variance) Route A Route B 5.9004.200 mean 1.402 1.800 std. dev 6 n 9 df 1.7000 difference (Route A - Route B) 2.6733 pooled variance 16350 pooled std. dev 0.9901 standard error of difference 0 hypothesized difference 172 t 1201 p-value (two-tailed) F-test for equality of variance 3.240 variance: Route B 1.965 variance: Route A 1.65 F 6484 p-value

d)

Since test statistics does not lie in rejection region so we fail to reject the null hypothesis.