Question

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 x1 = 3.00 cm, with sample standard deviation s1 = 0.80 cm. Another random sample of n2 = 46 stemless projectile points showed the mean length to be x2 = 2.69 cm, with s2 = 0.90 cm. 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 are we testing in this problem?

-single mean

-difference of proportions

-single proportion

-paired difference

-difference of means

b.) What is the level of significance? _____

c.)State the null and alternate hypotheses.

-H0: μ1 = μ2; H1: μ1 ≠ μ2

-H0: μ1 ≥ μ2; H1: μ1 < μ2

-H0: μ1 ≤ μ2; H1: μ1 > μ2

-H0: μ1 ≠ μ2; H1: μ1 = μ2

d.) What sampling distribution will you use? What assumptions are you making?

-The Student's t. We assume that both population distributions are approximately normal with unknown population standard deviations.

-The standard normal. We assume that both population distributions are approximately normal with unknown population standard deviations.

-The standard normal. We assume that both population distributions are approximately normal with known population standard deviations.

-The Student's t. We assume that both population distributions are approximately normal with known population standard deviations.

e.) What is the value of the sample test statistic? (Test the difference μ1 − μ2. Round your answer to three decimal places.)

f.) Estimate the P-value.

-P-value > 0.500

-0.250 < P-value < 0.500

-0.100 < P-value < 0.250

-0.050 < P-value < 0.100

-0.010 < P-value < 0.050

-P-value < 0.010

g.) Sketch the sampling distribution and show the area corresponding to the P-value.

h.) Will you reject or fail to reject the null hypothesis? Are the data statistically significant at level α?

-At the α = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.

-At the α = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.

-At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.

-At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.

i.) Interpret your conclusion in the context of the application.

-There is sufficient evidence at the 0.05 level to conclude that there is a difference in mean length of the two types of projectile points.

-There is insufficient evidence at the 0.05 level to conclude that there is a difference in mean length of the two types of projectile points.

Answer 1