Question

Buckling Up. The National Highway Traffic Safety Administration collects data on seat-belt use and publishes results in the document Occupant Restraint Use. Of 1000 drivers $16-24$ years old, $79\%$ said that they buckle up, whereas 924 of 1100 drivers 25-69 years old said that they did. At the $1\%$significance level, do the data provide sufficient evidence to conclude that there is a difference in seat-belt use between the two age groups?

Short answer

The data provide sufficient evidence to conclude that there is a sufficient difference in seat-belt use between the two age groups.

Step-by-step solution

Given Information

The given values are,

$$\begin{gathered} x_1=792, \\ {n}_1=1000, \\ {x}_2=924, \\ {n}_2=1100, \\ \alpha =0.01 \end{gathered}$$

Explanation

The null hypothesis.

$H_0:p_1=p_2$

The null hypothesis.

$H_a:p_1\ne p_2$

Calculate the value of test statistics and $p$- values by using MINITAB.

MINITAB output:

Test and $\mathrm{Cl}$for two proportions.

From the MINITAB output, the test statistic is $-2.95$and the $p$- value $0.003$.

The significance level $alpha=0.01.$

The $p$-value is lesser than the level of significance.

$p\text{- value}(=0.003)<(=0.01).$

Using the rejection rule, it can be concluded that there is evidence to reject the null hypothesis $\left(H_0\right)$at $alpha=0.01.$

The data show that there is a significant difference in seat belt use between the two age groups.

As a result, the data provide enough evidence to conclude that there is a significant difference in seat belt use between the two age groups.