In this problem, assume that the distribution of differences is approximately no

Question

In this problem, assume that the distribution of differences is approximately normal. Note: 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. The artifact frequency for an excavation of a kiva in Bandelier National Monument gave the following information. Stratum Flaked Stone Tools Nonflaked Stone Tools 1 4 1 2 8 6 3 8 4 4 1 3 5 4 7 6 38 32 7 51 30 8 25 12 Does this information indicate that there tend to be more flaked stone tools than nonflaked stone tools at this excavation site? Use a 10% level of significance. (Let d = flaked nonflaked.) (a) What is the level of significance? Correct: Your answer is correct. . State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test? H0: d = 0; H1: d > 0; right-tailed H0: d = 0; H1: d 0; two-tailed H0: d > 0; H1: d = 0; right-tailed H0: d = 0; H1: d < 0; left-tailed (b) What sampling distribution will you use? What assumptions are you making? The Student's t. We assume that d has an approximately uniform distribution. The Student's t. We assume that d has an approximately normal distribution. The standard normal. We assume that d has an approximately normal distribution. The standard normal. We assume that d has an approximately uniform distribution. What is the value of the sample test statistic? (Round your answer to three decimal places.) (c) Find (or estimate) the P-value. (Round your answer to four decimal places.) Sketch the sampling distribution and show the area corresponding to the P-value. Maple Generated Plot Maple Generated Plot Maple Generated Plot Maple Generated Plot (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 ? At the = 0.10 level, we reject the null hypothesis and conclude the data are not statistically significant. At the = 0.10 level, we reject the null hypothesis and conclude the data are statistically significant. At the = 0.10 level, we fail to reject the null hypothesis and conclude the data are not statistically significant. At the = 0.10 level, we fail to reject the null hypothesis and conclude the data are statistically significant. (e) State your conclusion in the context of the application. Reject the null hypothesis, there is sufficient evidence to claim that the average number of flaked stone tools is higher. Fail to reject the null hypothesis, there is insufficient evidence to claim that the average number of flaked stone tools is higher. Reject the null hypothesis, there is insufficient evidence to claim that the average number of flaked stone tools is higher. Fail to reject the null hypothesis, there is sufficient evidence to claim that the average number of flaked stone tools is higher.

Explanation / Answer

Using Minitab:

Null and alternative Hypothesis:

H0: d = 0; H1: d > 0

We can use here paired t test.

Paired T-Test and CI: Flaked, Nonflaked

Paired T for Flaked - Nonflaked

N Mean StDev SE Mean
Flaked 8 17.38 18.58 6.57
Nonflaked 8 11.88 12.25 4.33
Difference 8 5.50 7.98 2.82

90% lower bound for mean difference: 1.51
T-Test of mean difference = 0 (vs > 0): T-Value = 1.95 P-Value = 0.046

P-value 0.046 <0.1 we reject null hypothesis. We conclude that here tend to be more flaked stone tools than nonflaked stone tools at this excavation site.

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