Reference no: EM132851156
The following table shows site type and type of pottery for a random sample of 628 sherds at an archaeological location.Pottery TypeSite TypeMesa Verde
Black-on-WhiteMcElmo
Black-on-WhiteMancos
Black-on-WhiteRow TotalMesa Top 806247189 Cliff-Talus 827457213 Canyon Bench 957358226 Column Total257209162628 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 not independent.
H1: Site type and pottery are independent. H0: Site type and pottery are independent.
H1: Site type and pottery are not 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? Uniform chi-square normal binomial Student's t
What are the degrees of freedom? 3
(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 > ?, 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 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.