Random samples of 49 male students and 50 female students at the U of A were asked to state their car preference (American, European, and Japanese). The resulting frequencies are shown in the following table. Is there enough evidence to conclude a difference in car preference between males and females? American European Japanese Male 16 13 20 Female 10 23 17 (a) In performing this statistical test, state the hypotheses. O Ho: the distribution of preference is not the same for males and females vs. Ha: the distribution of preference is the same for males and females Ho: the proportion of females is the same for each car preference vs. Ha: the proportion of females is not the same for each car preference Ho: the distribution of gender is not the same for each car preference vs. Ha: the distribution of gender is the same for each car preference O Ho: the distribution of preference is the same for males and females vs. Ha: the distribution of preference is not the same for males and females O Ho: the proportion of males is the same for each car preference vs. Ha: the proportion of males is not the same for each car preference (b) What is the expected frequencies of each cell? Fill out the table. (Round your answers to 2 decimal places, if needed.) American European Japanese Male 12.87 Female 18.69 (c) What is the test statistic value for this hypothesis test? (Round your answers to 2 decimal places, if needed.) TS = (d) The test statistic follows a chi-square distribution with df = 2 + (e) Using the statistical table, the p-value is 0 < p-value < 0.005 (f) Based on the p-value, those conducting the test should fail to reject the null hypothesis at the significance level of 0.05. (g) What is the appropriate conclusion? There is sufficient evidence to conclude there is a difference in males and females for car preference. There is insufficient evidence to conclude the proportion of males is not the same for each car preference. There is sufficient evidence to conclude there is no difference in males and females for car preference. There is insufficient evidence to conclude there is a difference in males and females for car preference. There is sufficient evidence to conclude the proportion of males is not the same for each car preference. Olivia attends school at the University of Alberta and decides to compile a contingency table of students who are taking various degrees. She surveys a group of students, and the data she collects is listed in the contingency table below. Olivia want to see if degree and gender are dependent variables. PhD Masters Undergraduate Male 18 20 75 Female 12 25 70 (a) In performing this statistical test, state the hypotheses. O Ho: The proportion of female students is the same as the proportion of male students vs. Ha: The proportion of female students is not the same as the proportion of male students O Ho: Degree and gender are dependent vs. Ha: Degree and gender are independent Ho: Degree and gender are independent vs. Ha: Degree and gender are dependent O Ho: Degree is associated with gender vs. Ha: Degree is not associated with gender O Ho: Degree is related to gender vs. Ha: Degree is not related to gender (b) What is the expected frequencies of each cell? Fill out the table. (Round your answers to 2 decimal places, if needed.) PhD Masters Undergraduate Male 15.41 Female 70.52 (c) What is the test statistic value for this hypothesis test? (Round your answers to 2 decimal places, if needed.) TS = (d) The test statistic follows a chi-square distribution with df = 2 (e) Using the statistical table, the p-value is 0.01 < p-value < 0.025 (f) Based on the p-value, those conducting the test should fail to reject the null hypothesis at the significance level of 0.05. (g) What is the appropriate conclusion? There is sufficient evidence to conclude degree and gender are independent. There is sufficient evidence to conclude the proportion of females is not the same for each degree. There is insufficient evidence to conclude degree and gender are dependent. There is insufficient evidence to conclude degree and gender are independent. There is sufficient evidence to conclude degree and gender are dependent.