Question

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 79 58 52 189 Cliff-Talus 80 71 62 213 Canyon Bench 94 70 62 226 Column Total 253 199 176 628 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 independent. H1: Site type and pottery are not independent. 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. (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 Student's t 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.

Answer 1

Solution: (a) What is the level of significance?

Answer: The level of significance is

State the null and alternate hypotheses.

Answer:

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.)

Answer:

The chi-square statistic is given below:

The observed frequencies are given below:

The expected frequencies are given below:

Therefore, the chi-square statistic is given below:

Therefore, the value of the chi-square statistic for the sample is

Are all the expected frequencies greater than 5?

Answer: Yes

What sampling distribution will you use?

Answer: Chi-square

What are the degrees of freedom?

Answer:

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

Answer: p-value > 0.100

Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis of independence?

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

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

Answer: At the 1% level of significance, there is insufficient evidence to conclude that site and pottery type are not independent.