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	9	2
2	10	4
3	7	3
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 5% level of significance. (Let d = flaked − nonflaked.)

(a) What is the level of significance?


State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test?

H₀: μ_d = 0; H₁: μ_d ≠ 0; two-tailedH₀: μ_d = 0; H₁: μ_d < 0; left-tailed     H₀: μ_d = 0; H₁: μ_d > 0; right-tailedH₀: μ_d > 0; H₁: μ_d = 0; right-tailed

(b) What sampling distribution will you use? What assumptions are you making?

The standard normal. We assume that d has an approximately normal distribution.The standard normal. We assume that d has an approximately uniform distribution.     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.

What is the value of the sample test statistic? (Round your answer to three decimal places.)


(c) Find (or estimate) the P-value.

P-value > 0.2500.125 < P-value < 0.250     0.050 < P-value < 0.1250.025 < P-value < 0.0500.005 < P-value < 0.025P-value < 0.005

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 α?

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

(e) State your conclusion in the context of the application.

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 sufficient 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.Fail to reject the null hypothesis, there is insufficient evidence to claim that the average number of flaked stone tools is higher.

Answer 1

a)
0.05 is alpha

H0: μd = 0; H1: μd > 0; right-tailed

b)

We assume that d has an approximately normal distribution.

Test statistic,
t = (dbar - 0)/(s(d)/sqrt(n))
t = (6.5 - 0)/(7.7644/sqrt(8))
t = 2.368

c)

P-value Approach
P-value = 0.0249

0.125 < P-value < 0.250
As P-value < 0.05, reject the null hypothesis.

d)

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

e)

Reject the null hypothesis, there is sufficient evidence to claim that the average number of flaked stone tools is higher.