Question

Nationally, roughly 14% of adults fail to wear their seatbelt on every car trip. Suppose we find that 6 of 31 drivers in Rochester are not wearing their seatbelt

a) What sample proportion of drivers weren't wearing their belt?

b) Run the following hypothesis test from your sample. (z^ * =1.650 1-tai )

H 0 : p=0.14

H A: p>0.14

c) Explain what your conclusion means in the context of this situation.

Answer 1

a) n = 31 , X = 6

The sample proportion p^ = 6/31 = 0.19

p^ = 0.19

b ) we have to test

Ho : p = 0.14

Ha : p > 0.14

Test statistic Z

Z = (p^ - p)/sqrt[p*q/n]

Z = (0.19-0.14)/sqrt [0.14*0.86/31]

Z = 0.80

Given Zcritical Z* = 1.65

Decision rule : If Z > Z* we reject the null hypothesis otherwise we fail to reject the null hypothesis

Our Z = 0.80 < 1.65

Decision : fail to reject the null hypothesis

c) conclusion : There is no sufficient evidence to support the claim that 14% of adults fail to wear their seatbelt on every car trip