The Wind Mountain archaeological site is in southwest New Mexico. Prehistoric Native Americans called Anasazi once lived and hunted small game in this region. A stemmed projectile point is an arrowhead that has a notch on each side of the base. Both stemmed and stemless projectile points were found at the Wind Mountain site. A random sample of n₁ = 55 stemmed projectile points showed the mean length to be x̅₁ = 3.0 cm, with sample standard deviation s₁ = 0.8cm. Another random sample of n₂ = 51 stemless projectile points showed the mean length to be x̅₂ = 2.7cm, with s₂ = 0.9cm Do these data indicate a difference (either way) in the population mean length of the two types of projectile points? Use a 5% 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 distribution value.

(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 by a small amount and therefore produce a slightly more “conservative” answer. Answers may vary due to rounding.