Question

In: Statistics and Probability

The types of raw materials used to construct stone tools found at an archaeological site are...

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% 893
Obsidian 10.6% 153
Welded Tuff 11.4% 183
Pedernal chert 13.1% 212
Other 3.6% 45

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 the same.
H1: The distributions are different.    

H0: The distributions are the same.
H1: The distributions are the same.

H0: The distributions are different.
H1: The distributions are the same.


(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?


What sampling distribution will you use?

normal

chi-square   

binomial

uniform

Student's t


What are the degrees of freedom?


(c) Find or estimate the P-value of the sample test statistic.

P-value > 0.1000

.050 < P-value < 0.100

  0.025 < P-value < 0.050

0.010 < P-value < 0.0250

.005 < P-value < 0.010

P-value < 0.005


(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 > α, we fail to reject the null hypothesis.

Since the P-value > α, we reject the null hypothesis.    

Since the P-value ≤ α, we reject the null hypothesis.

Since the P-value ≤ α, we fail to reject the null hypothesis.


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

At the 0.01 level of significance, the evidence is sufficient to conclude that the regional distribution of raw materials does not fit the distribution at the current excavation site.

At the 0.01 level of significance, the evidence is insufficient to conclude that the regional distribution of raw materials does not fit the distribution at the current excavation site.    

Solutions

Expert Solution

a.

H0: The distributions are the same.
H1: The distributions are different.  

b. Chi-Square statistic = 4.466

Yes, All expected frequencies are greater than 5.

The sampling distribution of test statistic is Chi-Square distribution having 4 degrees of freedom.

c,

P-value>0.100

d. Since the P-value > α, we fail to reject the null hypothesis.

e.

At the 0.01 level of significance, the evidence is insufficient to conclude that the regional distribution of raw materials does not fit the distribution at the current excavation site.    

Thank You.

Please, give thumbs up.


Related Solutions

The types of raw materials used to construct stone tools found at an archaeological site are...
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% 890 Obsidian 10.6% 162 Welded Tuff 11.4% 175 Pedernal chert 13.1% 212 Other 3.6% 47 Use a 1% level of significance to test the claim that the regional distribution of raw...
The types of raw materials used to construct stone tools found at an archaeological site are...
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% 900 Obsidian 10.6% 153 Welded Tuff 11.4% 165 Pedemal chert 13.1% 215 Other 3.6% 53 Use a 1% level of significance to test the claim that the regional distribution of raw...
The types of raw materials used to construct stone tools found at an archaeological site are...
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% 925 Obsidian 10.6% 154 Welded Tuff 11.4% 174 Pedernal chert 13.1% 189 Other 3.6% 44 Use a 1% level of significance to test the claim that the regional distribution of raw...
The types of raw materials used to construct stone tools found at an archaeological site are...
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% 894 Obsidian 10.6% 152 Welded Tuff 11.4% 178 Pedemal chert 13.1% 217 Other 3.6% 45 Use a 1% level of significance to test the claim that the regional distribution of raw...
The types of raw materials used to construct stone tools found at an archaeological site are...
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% 904 Obsidian 10.6% 165 Welded Tuff 11.4% 163 Pedernal chert 13.1% 209 Other 3.6% 45 Use a 1% level of significance to test the claim that the regional distribution of raw...
The types of raw materials used to construct stone tools found at an archaeological site are...
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% 888 Obsidian 10.6% 157 Welded Tuff 11.4% 180 Pedernal chert 13.1% 208 Other 3.6% 53 Use a 1% level of significance to test the claim that the regional distribution of raw...
The types of raw materials used to construct stone tools found at an archaeological site are...
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% 899 Obsidian 10.6% 168 Welded Tuff 11.4% 177 Pedemal chert 13.1% 180 Other 3.6% 62 Use a 1% level of significance to test the claim that the regional distribution of raw...
The types of raw materials used to construct stone tools found at an archaeological site are...
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% 910 Obsidian 10.6% 161 Welded Tuff 11.4% 173 Pedernal chert 13.1% 185 Other 3.6% 57 Use a 1% level of significance to test the claim that the regional distribution of raw...
The types of raw materials used to construct stone tools found at an archaeological site are...
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% 914 Obsidian 10.6% 154 Welded Tuff 11.4% 157 Pedernal chert 13.1% 202 Other 3.6% 59 Use a 1% level of significance to test the claim that the regional distribution of raw...
The types of raw materials used to construct stone tools found at an archaeological site are...
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% 898 Obsidian 10.6% 163 Welded Tuff 11.4% 165 Pedernal chert 13.1% 197 Other 3.6% 63 Use a 1% level of significance to test the claim that the regional distribution of raw...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT