(a) What is the level of significance? State the null and alternate hypotheses. H0: Myers-Briggs preference and profession are not independent H1: Myers-Briggs preference and profession are not independent.H0: Myers-Briggs preference and profession are independent H1: Myers-Briggs preference and profession are not independent.    H0: Myers-Briggs preference and profession are independent H1: Myers-Briggs preference and profession are independent.H0: Myers-Briggs preference and profession are not independent H1: 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? YesNo     What sampling distribution will you use? normaluniform    binomialchi-squareStudent's t 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.) (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 5% level of significance, there is insufficient evidence to conclude that Myers-Briggs preference and the profession are not independent.At the 5% level of significance, there is sufficient evidence to conclude that Myers-Briggs preference and the profession are not independent.

The following table shows the Myers-Briggs personality preferences for a random sample of 406 people in the listed professions. E refers to extroverted and I refers to introverted.   Personality Type   Occupation E I Row Total Clergy (all denominations) 59 48 107 M.D. 72 90 162 Lawyer 51 86 137 Column Total 182 224 406 Use the chi-square test to determine if the listed occupations and personality preferences are independent at the 0.05 level of significance. (a) What is the level of significance?   (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.)   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.)

A sociologist studying New York City ethnic groups wants to determine if there is a difference in income for immigrants from four different countries during their first year in the city. She obtained the data in the following table from a random sample of immigrants from these countries (incomes in thousands of dollars). Use a 0.05 level of significance to test the claim that there is no difference in the earnings of immigrants from the four different countries. Country I Country II Country III Country IV 12.3 8.3 20.4 17.3 9.1 17.2 16.5 8.7 10.9 19.2 22.8 14.2 8.8 10.2 5.5 21.4 16.1   19.2 19.3   (b) Find SSTOT, SSBET, and SSW and check that SSTOT = SSBET + SSW. (Round your answers to three decimal places.) SSTOT =   SSBET =   SSW =   Find d.f.BET, d.f.W, MSBET, and MSW. (Round your answer to three decimal places for MSBET and MSW.) dfBET =   dfW =   MSBET =   MSW =   Find the value of the sample F statistic. (Round your answer to three decimal…

The following data said shows the bank account balance for a random sample of 17 IRSC students.  Round solution to two decimal places if necessary. What is the mean of this data set? Mean= What is the median of this data set? Median= What is the mode of this data set if no modes exist type DNE. if multiple modes exist enter the values in a comma separated lists Mode=