An insurance company collects data on seat-belt use among drivers in a country.

Question

An insurance company collects data on seat-belt use among drivers in a country. Of 1500 drivers 25-34 years old, 32% said that they buckle up, whereas 430 of 1803 drivers 50-59 years old said that they did. At the 10% significance level, do the data suggest that there is a difference in seat-belt use between drivers 25-34 years old and those 50-59? Let population 1 be drivers of age 25-34 and let population 2 be drivers of age 50-59. Use the two-proportions z-test to conduct the required hypothesis test What are the hypotheses for this lest? A. H_0: p_1 = p_2 H_a: p_1 > p_2 B. H_0: p_1 = p_2 H_a: p_1

Explanation / Answer

The statistical software output for this problem is:

Two sample proportion summary hypothesis test:
p1 : proportion of successes for population 1
p2 : proportion of successes for population 2
p1 - p2 : Difference in proportions
H0 : p1 - p2 = 0
HA : p1 - p2 0

Hypothesis test results:

Hence,

Hypotheses: Option C is correct.

z = 5.19

P = 0.000

Conclusion: Option C is correct.

Difference Count1 Total1 Count2 Total2 Sample Diff. Std. Err. Z-Stat P-value p1 - p2 480 1500 430 1800 0.081111111 0.015623589 5.1915801 <0.0001

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