A random sample of n₁ = 288 voters registered in the state of California showed that 141 voted in the last general election. A random sample of n₂ = 216 registered voters in the state of Colorado showed that 125 voted in the most recent general election. Do these data indicate that the population proportion of voter turnout in Colorado is higher than that in California? Use a 5% level of signi­ficance.

(a) What is the level of signi­ficance? State the null and alternate hypotheses.

(b) Check Requirements What sampling distribution will you use? What assumptions are you making? Compute the sample test statistic and corresponding z or t value as appropriate.

(c) Find (or estimate) the P-value. Sketch the sampling distribution and show the area corresponding to the P-value.

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically signifi­cant at level a?

(e) Interpret your conclusion in the context of the application.

For degrees of freedom d.f. not in the Student’s t table, use the closest d.f. that is smaller. In some situations, this choice of d.f. may increase the P-value a small amount and therefore produce a slightly more “conservative” answer.

Answers may vary due to rounding.