Archaeology: Arrowheads 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 = 55stemmed projectile points showed the mean length to be x1 = 3.0 cm, with sample standard deviation s1 = 0.8 cm. Another random sample of n12 = 51stemless projectile points showed the mean length to be x2 = 2.7 cm, with s2 = 0.9 cm (Source: Mimbres Mogollon Archaeology, by A. I. Woosley and A. J. McIntyre, University of New Mexico Press). 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.
Assume that the distribution of population means for both stem and stemless projectile arrowheads are normally distributed.
1) Find the value of the test statistic for this hypothesis test._____________________
2) Find the critical value for this hypothesis test.____________________
3) Find the P-value for this hypothesis test. (Use your calculator) ________________________
4) Write the conclusion for this hypothesis test.
Choose from the following _______________
A. Reject the null hypothesis. There is sufficient evidence that the population mean lengths of these two types of projectile points are different.
B. Fail to reject the null hypothesis. There is insufficient evidence that the population mean lengths of these two types of projectile points are different.
C. Fail to reject the null hypothesis. There is sufficient evidence that the population mean lengths of these two types of projectile points are the same.
D. Reject the null hypothesis. There is insufficient evidence that that the population mean lengths of these two types of projectile points are the same.
5) Compare the critical region method conclusion with the one obtained by using the P-value method. Are they the same? Select the correct answer: ________________
A. The conclusions obtained by using both methods are the same.
B. We reject the null hypothesis using the critical region method, but fail to reject using the P-value method.
C. We reject the null hypothesis using