This problem is based on information taken from Life in America’s Fifty States by G. S. Thomas. A random sample of n₁ = 153 people ages 16 to 19 was taken from the island of Oahu, Hawaii, and 12 were found to be high school dropouts. Another random sample of n₂ = 128 people ages 16 to 19 was taken from Sweetwater County, Wyoming, and 7 were found to be high school dropouts. Do these data indicate that the population proportion of high school dropouts on Oahu is different (either way) from that of Sweetwater County? Use a 1% level of signifi­cance.

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

(b) 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.