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 level of significance?
State the null and alternate hypotheses.
H0: Site type and pottery are not
independent.
H1: Site type and pottery are not
independent.
H0: Site type and pottery are
independent.
H1: Site type and pottery are
independent.
H0: Site type and pottery are
independent.
H1: Site type and pottery are not
independent.
H0: Site type and pottery are not
independent.
H1: Site type and pottery are independent.
(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?
Yes
No
What sampling distribution will you use?
Student's t
uniform binomial
normal
chi-square
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.)
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 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 1% level of significance, there is sufficient evidence to conclude that site and pottery type are not independent.
At the 1% level of significance, there is insufficient evidence to conclude that site and pottery type are not independent.
The statistical software output for this problem is:
Hence,
a) Level of significance = 0.01
Hypotheses: H0: Site type and pottery are
independent.
H1: Site type and pottery are not
independent.
b) Test statistic = 0.991
Yes
Chi - square
Degrees of freedom = 4
c) p-value > 0.100
d) Since the P-value > α, we fail to reject the null hypothesis.
e) At the 1% level of significance, there is insufficient evidence to conclude that site and pottery type are not independent.
The following table shows site type and type of pottery for a random sample of 628...
The following table shows site type and type of pottery for a random sample of 628 sherds at an archaeological location. Pottery Type Mesa Verde McElmo Mancos Site Type Black White Black-on-White Row Total Black-on-White | Mesa Top 77T 189 Cliff-Talus 81 213 Canyon Bench 226 Column Total 248 207 173 628 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 level of significance? -...
The following table shows site type and type of pottery for a random sample of 628 sherds at an archaeological location. 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 level of significance? State the null and alternate hypotheses Ho: Site type and pottery are not independent. Hy: Site type and pottery are not independent. Ho: Site type and pottery are independent. Hy: Site type...
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The following table shows ceremonial ranking and type of pottery sherd for a random sample of 434 sherds at an archaeological location. Ceremonial Ranking Cooking Jar Sherds Decorated Jar Sherds (Noncooking) Row Total A 91 44 135 B 96 49 145 C 74 80 154 Column Total 261 173 434 Use a chi-square test to determine if ceremonial ranking and pottery type are independent at the 0.05 level of significance. (a) What is the level of significance? State the null...
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