Question

Let p equal the proportion of drivers who use a seat belt in a state that does not have a mandatory seat belt law. It was claimed that p = 0.14. An advertising campaign was conducted to increase this proportion. Two months after the campaign, y = 104 out of a random sample of n = 590 drivers were wearing their seat belts. Do an appropriate hypothesis test (show the 6-steps) to see if the campaign was successful. Use 5% significance level to draw a conclusion.

Answer 1

a)

Hypothesis

H0: p = 0.14

Ha: p > 0.14

Sample proportion = y / n = 104 / 590 = 0.1763

b)

Test statistics

z = - p / sqrt( p (1 -p ) / n)

= 0.1763 - 0.14 / sqrt( 0.14 * 0.86 / 590)

= 2.54

This is test statistics value.

c)

Critical region -

Critical value at 0.05 level is 1.645

Rejection region - Reject H0 if test statistics > 1.645

d)

Decision -

Since test statistics > 1.645, we have sufficient evidence to reject H0.

e)

p-value = P( Z > z)

= P( Z > 2.54)

= 0.0055

f)

Conclusion -

We conclude at 0.05 level that we have enough evidence to support the claim that campaign was successful.