Please clearly highlight answers with short explanations.

PART A

The following table shows age distribution and location of a random sample of 166 buffalo in a national park. - Lamar District Nez Perce District Row Total Calf ll 15 15 4]. Yearling 9 13 11 Adult 31 3O 31 Column Total IA use SALT Use a chi-square test to determine if age distribution and location are independent at the 0.05 level ofsignificance. {a} What is the level of signicance? :l State the null and alternate hypotheses. O HO: Age distribution and location are not independent. H1: Age distribution and location are not independent. C3- Ho: Age distribution and location are independent. H1: Age distribution and location are not independent. C3- Ho: Age distribution and location are not independent. H1: Age distribution and location are independent. 0 H0: Age distribution and location are independent. H1: Age distribution and location are independent. {b} Find the value of the chisquare statistic for the sample. {Round the expected frequencies to at least three decimal places. Round the test statistic to three decimal places.) :I Are all the expected frequencies greater than 5? C'- Yes C?- No What sampling distribution will you use? C3- binomial C- uniform C3- chi-square C'- Student's 1" C3- normal 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.) O p-value > 0.100 O 0.050 a, we fail to reject the null hypothesis. O Since the P-value > a, we reject the null hypothesis. O Since the P-value s a, we reject the null hypothesis. O Since the P-value s a, we fail to reject the null hypothesis. (e) Interpret your conclusion in the context of the application. O At the 5% level of significance, there is sufficient evidence to conclude that age distribution and location are not independent. O At the 5% level of significance, there is insufficient evidence to conclude that age distribution and location are not independent.The following table shows the Myers-Briggs personality preference and area of study for a random sample of 519 college students. In the table, IN refers to introvert, intuitive; EN refers to extrovert, intuitive; IS refers to introvert, sensing; and ES refers to extrovert, sensing. Myers-Briggs Preference Arts & Science Business Allied Health Row Total IN 60 12 24 96 77 44 33 154 57 40 18 115 71 44 39 154 Column Total 265 140 114 519 L USE SALT Use a chi-square test to determine if Myers-Briggs preference type is independent of area of study at the 0.05 level of significance. (a) What is the level of significance? State the null and alternate hypotheses. O H: Myers-Briggs type and area of study are independent. Hy: Myers-Briggs type and area of study are not independent. O Ho: Myers-Briggs type and area of study are not independent. H. : Myers-Briggs type and area of study are independent. O Ho: Myers-Briggs type and area of study are not independent. H : Myers-Briggs type and area of study are not independent. O H: Myers-Briggs type and area of study are independent. Hi : Myers-Briggs type and area of study 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? O Yes O No What sampling distribution will you use? O uniform O normal O Student's t O binomial O chi-squareWhat are the degrees of freedom? (c) Find or estimate the P-value of the sample test statistic. (Round your answer to three decimal places.) O p-value > 0.100 O 0.050 a, we fail to reject the null hypothesis. O Since the P-value > a, we reject the null hypothesis. O Since the P-value s a, we reject the null hypothesis. Since the P-value s a, we fail to reject the null hypothesis. (e) Interpret your conclusion in the context of the application. O At the 5% level of significance, there is sufficient evidence to conclude that Myers-Briggs type and area of study are not independent. O At the 5% level of significance, there is insufficient evidence to conclude that Myers-Briggs type and area of study are not independent