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% | 881 |
Obsidian | 10.6% | 162 |
Welded Tuff | 11.4% | 171 |
Pedemal chert | 13.1% | 209 |
Other | 3.6% | 63 |
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 the same.
H1: The distributions are the
same.H0: The distributions are different.
H1: The distributions are the
same. H0: The
distributions are different.
H1: The distributions are
different.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-squarebinomial normaluniformStudent's t
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.
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% 924 Obsidian 10.6% 151 Welded Tuff 11.4% 166 Pedernal chert 13.1% 190 Other 3.6% 55 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 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% 906 Obsidian 10.6% 160 Welded Tuff 11.4% 160 Pedernal chert 13.1% 205 Other 3.6% 55 Use a 1% level of significance to test the claim that the regional distribution of raw...
The type of household for the U.S. population and for a random sample of 411 households from a community in Montana are shown below. Type of Household Percent of U.S. Households Observed Number of Households in the Community Married with children 26% 101 Married, no children 29% 118 Single parent 9% 28 One person 25% 97 Other (e.g., roommates, siblings) 11% 67 Use a 5% level of significance to test the claim that the distribution of U.S. households fits the...
The type of household for the U.S. population and for a random sample of 411 households from a community in Montana are shown below. Type of Household Percent of U.S. Households Observed Number of Households in the Community Married with children 26% 100 Married, no children 29% 118 Single parent 9% 30 One person 25% 93 Other (e.g., roommates, siblings) 11% 70 Use a 5% level of significance to test the claim that the distribution of U.S. households fits the...
The age distribution of the Canadian population and the age distribution of a random sample of 455 residents in the Indian community of a village are shown below. Age (years) Percent of Canadian Population Observed Number in the Village Under 5 7.2% 43 5 to 14 13.6% 73 15 to 64 67.1% 297 65 and older 12.1% 42 Use a 5% level of significance to test the claim that the age distribution of the general Canadian population fits the age...
The age distribution of the Canadian population and the age distribution of a random sample of 455 residents in the Indian community of a village are shown below. Age (years) Percent of Canadian Population Observed Number in the Village Under 5 7.2% 43 5 to 14 13.6% 73 15 to 64 67.1% 297 65 and older 12.1% 42 Use a 5% level of significance to test the claim that the age distribution of the general Canadian population fits the age...
The following table shows site type and type of pottery for a random sample of 628 sherds at an archaeological location. Pottery Type Site Type Mesa Verde Black-on-White McElmo Black-on-White Mancos Black-on-White Row Total Mesa Top 70 59 60 189 Cliff-Talus 82 69 62 213 Canyon Bench 91 73 62 226 Column Total 243 201 184 628 Use a chi-square test to determine if site type and pottery type are independent at the 0.01 level of significance. (a) What is...
The accuracy of a census report on a city in southern California was questioned by some government officials. A random sample of 1215 people living in the city was used to check the report, and the results are shown below. Ethnic Origin Census Percent Sample Result Black 10% 130 Asian 3% 35 Anglo 38% 462 Latino/Latina 41% 516 Native American 6% 62 All others 2% 10 Using a 1% level of significance, test the claim that the census distribution and...
The Fish and Game Department stocked a lake with fish in the following proportions: 30% catfish, 15% bass, 40% bluegill, and 15% pike. Five years later it sampled the lake to see if the distribution of fish had changed. It found that the 500 fish in the sample were distributed as follows. Catfish Bass Bluegill Pike 112 91 224 73 In the 5-year interval, did the distribution of fish change at the 0.05 level? (i) State the null and alternate...
The age distribution of the Canadian population and the age distribution of a random sample of 455 residents in the Indian community of a village are shown below. Age (years) Percent of Canadian Population Observed Number in the Village Under 5 7.2% 48 5 to 14 13.6% 79 15 to 64 67.1% 281 65 and older 12.1% 47 Use a 5% level of significance to test the claim that the age distribution of the general Canadian population fits the age...