Question

all 2018 (1) Protected View- Saved to this PC gn in Vehicles heading west on Front Street may turn right, left, or go straight ahead at Elm Street. The city traffic engineer believes that half of the vehicles will continue straight through the intersection. Of the remaining half, equal proportions will turn right and left. 200 vehicles were observed, resulting in the observed data below. 4. Vehicle Direction Straight Left Turn Right Turn Observed Frequency 112 48 40 Suppose we want to determine if there is evidence that the behavior of drivers at that intersection is different than what the city traffic engineer believes. To that end, use a chi-squared goodness- of-fit test to test the following hypotheses: Ho: The city traffic engineer's belief is correct. (50% go straight, 25% turn left, and 25% turn right) Hi The city traffic engineer's belief is not correct. (At least two percentages are different.) a. Determine the expected frequencies for the three categories. Vehicle Direction Straight Left Turn Right Turn Observed Frequency 112 48 40 Expected Frequency b. Determine the value of the test statistic. Using StatKey to find the p-value of the test. (To be more specific, use the x2 distribution, which is in the "Theoretical Distributions" row.) Copy a screenshot of the p-value into your assignment, and make sure the degrees of freedom box is not cropped out. c. d. Using a significance level of a -0.10, can we conclude that the engineer's belef is incorrect?

Answer 1

Ans:

a)

	Observed(fo)	Expected(fe)	(fo-fe)^2/fe
Straight	112	100	1.44
Left	48	50	0.08
Right	40	50	2
Total	200	200	3.52

Test statistic:

Chi square=3.52

b)df=3-1=2

p-value=CHIDIST(3.52,2)=0.1720

c)As,p-value>0.1,we fail to reject the null hypothesis.

There is not sufficient evidence to conclude that the engineer's belief is incorrect.