Question

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 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 LaTeX: \alphaα=0.05. What is the value of the test statistic used for this?

Answer 1

We conclude that 50% of the accidents would be caused by drunk driving.

Explanation:

We are given that the NSC claimed that 50% of the accidents would be caused by drunk driving.

A sample of 120 accidents showed that 67 were caused by drunk driving.

Let p = percentage of the accidents caused by drunk driving.

So, Null Hypothesis,
`H_0` : p = 50% {means that 50% of the accidents would be caused by drunk driving}

Alternate Hypothesis,
`H_A` : p
`\\eq` 50% {means that % of the accidents that would be caused by drunk driving is different from 50%}

The test statistics that would be used here One-sample z proportion statistics;

T.S. =
`\frac{\hat p-p}{\sqrt{(\hat p(1-\hat p))/(n) } }` ~ N(0,1)

where,
`\hat p` = sample proportion of accidents caused by drunk driving =
`(67)/(120)` = 0.56

n = sample of accidents = 120

So, test statistics =
`\frac{0.56-0.50}{\sqrt{(0.56(1-0.56))/(120) } }`

= 1.324

The value of z test statistics is 1.324.

Now, at 0.05 significance level the z table gives critical values of -1.96 and 1.96 for two-tailed test. Since our test statistics lies within the range of critical values of z, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which we fail to our null hypothesis.

Therefore, we conclude that 50% of the accidents would be caused by drunk driving.