Urgent- 2 sample hypothesis tests?

Question

In Dallas, some fire trucks were painted yellow to heighten their visibility. During a test period, the fleet of red fire trucks made 153,348 runs and had 20 accidents, while the fleet of yellow trucks made 135,035 runs and had 4 accidents. At a= .01, did the yellow fire trucks have a significantly lower accident rate?

(a) State the hypothesis

(b) state the rule an sketch it

(c) Find the sample proportions and z test statistic

(d) Make a decision

(e) Find the p-value and interpret it

(f) If statistically signficant,do you thinkthe difference is large enough to be important? If so, to hom and why?

(g) Is teh normaity assumption fulfilled? explain

Answer 1

Two-proportion z-test, equal variances

(a) H0: p1 - p2 = 0 versus H1: p1 - p2 ≠ 0

p1 = TRUE AVERAGE POPULATION PROPORTION OF ACCIDENTS FOR RED FIRE TRUCKS

p2 = TRUE AVERAGE POPULATION PROPORTION OF ACCIDENTS FOR YELLOW FIRE TRUCKS

(c) SAMPLE PROPORTIONS:

p1 = 0.000130422  RED FIRE TRUCK ACCIDENTS

p2 = 0.000029622 YELLOW FIRE TRUCK ACCIDENTS

Test Statistic formulae:

Two-proportion z-test, equal variances

http://en.wikipedia.org/wiki/Statistical...

Assumptions (for "Normality"):

n1 * p1 > 5 AND n1 * (1 − p1) > 5 and n2 * p2 > 5 and n2 * (1 − p2) > 5 and independent observations

Test and CI for Two Proportions

Sample   X       N  Sample p

1       20  153348  0.000130

2        4  135035  0.000030

Difference = p (1) - p (2)

Estimate for difference:  0.000100800

99.5% CI for difference:  (8.990763E-06, 0.000192610)

Test for difference = 0 (vs not = 0):  Z = 3.08  P-Value = 0.002

* NOTE * The normal approximation may be inaccurate for small samples.

Fisher's exact test: P-Value = 0.003

TEST STATISTIC: P-value < α/2 [0.003 < 0.05/2]

At 1% level of significance,  H0: p1 - p2 = 0 (Null Hypothesis stating there is zero difference between RED and YELLOW) should be rejected.

(f) There is a statistically significant difference between RED and YELLOW.

(g) "Normality" assumptions are not completely satisfied.

Why??

n2 * p2 > 5  [ 4 * 0.000029622 = 4] is not > 5