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 sample distribution agree.
(a) What is the level of significance?
State the null and alternate hypotheses.
H0: The distributions are the same.
H1: The distributions are
different.H0:
The distributions are different.
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?
YesNo
What sampling distribution will you use?
chi-square
uniform
Student's t
normal
binomial
What are the degrees of freedom?
(c) Estimate the P-value of the sample test statistic.
P-value > 0.100
0.050 < P-value <
0.100
0.025 < P-value < 0.050
0.010 < P-value < 0.025
0.005 < 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 that the population fits the
specified distribution of categories?
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 1% level of significance, the evidence is sufficient to
conclude that census distribution and the ethnic origin
distribution of city residents are different.
At the 1% level of significance, the evidence is insufficient to
conclude that census distribution and the ethnic origin
distribution of city residents are different.
The accuracy of a census report on a city in southern California was questioned by some...
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% 128 Asian 3% 45 Anglo 38% 478 Latino/Latina 41% 492 Native American 6% 60 All others 2% 12 Using a 1% level of significance, test the claim that the census distribution and...
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...
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% 52 5 to 14 13.6% 75 15 to 64 67.1% 282 65 and older 12.1% 46 Use a 5% level of significance to test the claim that the age distribution of the general Canadian population fits the age...
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 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...
He accuracy of a census report on a city is Southern California was questioned by some gov officials. A random sample of 1215 people living in the city was used to check the report and the results are shown here: Using a 1% level of significance, that the claim that census distribution and sample distribution agree. 3. The accuracy of a census report on a city is southern California was questioned by some government officials. A random sample of 1215...
A machine that puts corn flakes into boxes is adjusted to put an average of 15.3 ounces into each box, with standard deviation of 0.23 ounce. If a random sample of 15 boxes gave a sample standard deviation of 0.36 ounce, do these data support the claim that the variance has increased and the machine needs to be brought back into adjustment? (Use a 0.01 level of significance.) (i) Give the value of the level of significance. 0.01 State the...
Random samples of two species of iris gave the following petal lengths (in cm). x1, Iris virginica 5.1 5.9 4.5 4.9 5.7 4.8 5.8 6.4 5.7 5.9 x2, Iris versicolor 4.5 4.3 4.7 5.0 3.8 5.1 4.4 4.2 (a) Use a 5% level of significance to test the claim that the population standard deviation of x1 is larger than 0.55. What is the level of significance? State the null and alternate hypotheses. H0: σ = 0.55; H1: σ > 0.55...
The following table shows age distribution and location of a random sample of 166 buffalo in a national park. Age Lamar District Nez Perce District Firehole District Row Total Calf 13 13 15 41 Yearling 13 11 9 33 Adult 35 28 29 92 Column Total 61 52 53 166 Use a chi-square test to determine if age distribution and location are independent at the 0.05 level of significance. (a) What is the level of significance? State the null and...
A transect is an archaeological study area that is 1/5 mile wide and 1 mile long. A site in a transect is the location of a significant archaeological find. Let x represent the number of sites per transect. In a section of Chaco Canyon, a large number of transects showed that x has a population variance σ2 = 42.3. In a different section of Chaco Canyon, a random sample of 19 transects gave a sample variance s2 = 51.5 for...