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Use the chi-square test to determine iIf the listed occupations and personality preferences are independent at the 0.01 level of significance. (a) What is the level of significance? State the nul and alternate hypotheses. O Ha: Myers-Briggs preference and profession are nat independent. Hạ: Myers-Briggs preference and profession are not independent. O Ha: Myers-Briggs preference and profession are independent. Hạ: Myers-Briggs preference and profession are independent. O Hạ: Myers-Briggs preference and profession are independent. Hạ: Myers-Briggs preference and profession are not independent. O Ha: Myers-Briggs preference and profession are not independent. Hạ: Myers-Briggs preference and profession 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 Student's t O normal O uniform O binomial O chi-square What are the degrees of freedom? (c) Find or estimate the Avalue of the sample test statistic. O p-value > 0.100 O 0.050 < p-value <0.100 O D.025 < p-value < D.050 O 0.010 < p-value < 0.025 O 0.005 < p-value < 0.010 O p-value < 0.005

Use the chi-square test to determine iIf the listed occupations and personality preferences are independent at the 0.01 level of significance. (a) What is the level of significance? State the nul and alternate hypotheses. O Ha: Myers-Briggs preference and profession are nat independent. Hạ: Myers-Briggs preference and profession are not independent. O Ha: Myers-Briggs preference and profession are independent. Hạ: Myers-Briggs preference and profession are independent. O Hạ: Myers-Briggs preference and profession are independent. Hạ: Myers-Briggs preference and profession are not independent. O Ha: Myers-Briggs preference and profession are not independent. Hạ: Myers-Briggs preference and profession 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 Student's t O normal O uniform O binomial O chi-square What are the degrees of freedom? (c) Find or estimate the Avalue of the sample test statistic. O p-value > 0.100 O 0.050 < p-value <0.100 O D.025 < p-value < D.050 O 0.010 < p-value < 0.025 O 0.005 < p-value < 0.010 O p-value < 0.005

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.4: Distributions Of Data
Problem 19PFA
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The following table shows the Myers-Briggs personality preferences for a random sample of 519 people in the listed professions. T refers to thinking and F refers to feeling. Personality Type Occupation Clergy (all denominations) F Row Total 55 93 148 M.D. Lawyer Column Total 72 87 159 124 88 212 251 268 519 Use the chi-square test to determine if the listed occupations and personality preferences are independent at the 0.01 level of significance. (a) What is the level of significance? State the nul and alternate hypotheses. O Hg: Myers-Briggs preference and profession are not independent. H: Myers-Briggs preference and profession are not independent. O Hg: Myers-Briggs preference and profession are independent. H: Myers-Briggs preference and profession are independent. O Hg: Myers-Briggs preference and profession are independent. H: Myers-Briggs preference and profession are not independent. O Ha: Myers-Briggs preference and profession are not independent. Hz: Myers-Briggs preference and profession 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 57 O Yes O No What sampling distribution will you use? O student's t O normal O uniform O binomial O chi-square What are the degrees of freedom? (c) Find or estimate the Pvalue of the sample test statistic. O p-value > 0.100 O 0.050 < p-value <D.100 O D.025 < p-value < D.050 O D.010 < p-value < D.025 O 0.005 < p-value < D.010 O 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? O Since the P-value > a, we fall to reject the null hypothesis. O Since the P-value > a, we reject the null hypothesis. O Since the P-value sa, we reject the null hypothesis. O Since the P-value sa, we fall to reject the null hypothesis. (e) Interpret your condlusion in the context of the application. O At the 1% level of significance, there is insufficient evidence to conclude that Myers-Briggs preference and the profession are not independent. O At the 1% level of significance, there is sufficient evidence to condude that Myers-Briggs preference and the profession are not independent.
Transcribed Image Text:The following table shows the Myers-Briggs personality preferences for a random sample of 519 people in the listed professions. T refers to thinking and F refers to feeling. Personality Type Occupation Clergy (all denominations) F Row Total 55 93 148 M.D. Lawyer Column Total 72 87 159 124 88 212 251 268 519 Use the chi-square test to determine if the listed occupations and personality preferences are independent at the 0.01 level of significance. (a) What is the level of significance? State the nul and alternate hypotheses. O Hg: Myers-Briggs preference and profession are not independent. H: Myers-Briggs preference and profession are not independent. O Hg: Myers-Briggs preference and profession are independent. H: Myers-Briggs preference and profession are independent. O Hg: Myers-Briggs preference and profession are independent. H: Myers-Briggs preference and profession are not independent. O Ha: Myers-Briggs preference and profession are not independent. Hz: Myers-Briggs preference and profession 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 57 O Yes O No What sampling distribution will you use? O student's t O normal O uniform O binomial O chi-square What are the degrees of freedom? (c) Find or estimate the Pvalue of the sample test statistic. O p-value > 0.100 O 0.050 < p-value <D.100 O D.025 < p-value < D.050 O D.010 < p-value < D.025 O 0.005 < p-value < D.010 O 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? O Since the P-value > a, we fall to reject the null hypothesis. O Since the P-value > a, we reject the null hypothesis. O Since the P-value sa, we reject the null hypothesis. O Since the P-value sa, we fall to reject the null hypothesis. (e) Interpret your condlusion in the context of the application. O At the 1% level of significance, there is insufficient evidence to conclude that Myers-Briggs preference and the profession are not independent. O At the 1% level of significance, there is sufficient evidence to condude that Myers-Briggs preference and the profession are not independent.
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