The types of raw materials used to construct stone tools found at an archaeological site are shown below. A random sample of 1486 stone tools were obtained from a current excavation site.
Raw Material | Regional Percent of Stone Tools | Observed Number of Tools as Current excavation Site |
Basalt | 61.3% | 923 |
Obsidian | 10.6% | 153 |
Welded Tuff | 11.4% | 168 |
Pedemal chert | 13.1% | 181 |
Other | 3.6% | 61 |
Use a 1% level of significance to test the claim that the regional distribution of raw materials fits the distribution at the current excavation site.
(a) What is the level of significance?
State the null and alternate hypotheses.
H0: The distributions are different.
H1: The distributions are
different.H0: The distributions are
different.
H1: The distributions are the
same. H0: The
distributions are the same.
H1: The distributions are the
same.H0: The distributions are the same.
H1: The distributions are different.
(b) Find the value of the chi-square statistic for the sample.
(Round the expected frequencies to at least three decimal places.
Round the test statistic to three decimal places.)
Are all the expected frequencies greater than 5?
YesNo
What sampling distribution will you use?
chi-squareStudent's t uniformbinomialnormal
What are the degrees of freedom?
(c) Find or estimate the P-value of the sample test
statistic. (Round your answer to three decimal places.)
(d) Based on your answers in parts (a) to (c), will you reject or
fail to reject the null hypothesis of independence?
Since the P-value > ?, we fail to reject the null hypothesis.Since the P-value > ?, we reject the null hypothesis. Since the P-value ? ?, we reject the null hypothesis.Since the P-value ? ?, we fail to reject the null hypothesis.
(e) Interpret your conclusion in the context of the
application.
At the 0.01 level of significance, there is sufficient evidence to conclude that the regional distribution of raw materials and the current excavation site distribution are not independent.At the 0.01 level of significance, there is insufficient evidence to conclude that the regional distribution of raw materials and the current excavation site distribution are not independent.
p | Oi | Ei | (Oi-Ei)^2/Ei |
0.613 | 923 | 910.918 | 0.160250126 |
0.106 | 153 | 157.516 | 0.129474187 |
0.114 | 168 | 169.404 | 0.011636183 |
0.131 | 181 | 194.666 | 0.959384566 |
0.036 | 61 | 53.496 | 1.052602363 |
1 | 1486 | TS | 2.313347425 |
p-value | 0.678340011 |
a)
level of significance = 0.01
H0: The distributions are the same.
H1: The distributions are different.
b)
TS = 2.313347425
Are all the expected frequencies greater than 5?
Yes
What sampling distribution will you use?
chi-square
What are the degrees of freedom? = n-1 = 4
(c) Find or estimate the P-value of the sample test
statistic
0.678340011
d)
Since the P-value > ?, we fail to reject the null
hypothesis
e)
At the 0.01 level of significance, there is insufficient evidence
to conclude that the regional distribution of raw materials and the
current excavation site distribution are not independen
Get Answers For Free
Most questions answered within 1 hours.