Question

1.    For a Christmas and New Year’s week, the National Safety Council estimated that 500 people would be killed and 25,000 injured on the nation’s roads.  The NSC claimed that more than 50% of the accidents would be caused by drunk driving. A sample of 120 accidents showed that 67 were caused by drunk driving. Use these data to test the NSC’s claim with a = 0.05.

Answer 1

H0: p <= 0.50

Ha: p > 0.50 (Right tailed )

Sample proportion = 67 / 120 = 0.5583

Test statistics

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

= 0.5583 - 0.50 / sqrt( 0.50 * 0.50 / 120)

= 1.28

This is test statistics value.

Critical value at 0.05 level is 1.645

Since test statistics Z < 1.645, we do not have sufficient evidence to reject H0.

We conclude at 0.05 level that we fail to support the claim that more than 50% of the accidents

would be caused by drunk driving.