PART A

Is there an association between a gale being forecast and a gale actually being observed? The table below has some data on gales. Observed Not Observed Total Forecast 14 3 17 Not Forecast 12 124 136 Total 26 127 153 If the P-value of the chi-square two-way test for independence yields a value of 2.71 x 10714, which conclusion can you make? (Assume a = 0.05.) O There is sufficient evidence to reject H, and conclude that there is an association between a gale being forecast and a gale actually being observed. O There is insufficient evidence to reject H and conclude that there is not an association between a gale being forecast and a gale actually being observed. O There is sufficient evidence to reject H, and conclude that there is not an association between a gale being forecast and a gale actually being observed. O There is insufficient evidence to reject Hand conclude that there is an association between a gale being forecast and a gale actually being observed.A group of students were asked to name their favorite sporting event to attend at school. The results are shown below. Football Basketball Hockey Volleyball Total Male 28 21 15 5 69 Female 7 14 10 30 61 Total 35 35 25 35 130 Are the categories "gender" and "favorite sport" independent? (a) Determine whether the following statement is true or false. The chi-square test of independence can be used, since the observed counts are from a random sample and the sample is large enough. O True O False (b) Find the degrees of freedom for the test. (c) Calculate the y test statistic. (Round your answer to two decimal places.) (d) The P-value of the chi-square two-way test for independence yields a value P 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. At the 5% level of significance, there is insufficient evidence to conclude that Myers-Briggs preference and the profession are not independent. O At the 5% level of significance, there is sufficient evidence to conclude that Myers-Briggs preference and the profession are not independent