Add degrees of freedom

CHI SQUARE TESTS, INFE Alexia Chi-square test of independence Espanol Aragon Equipment, Inc. is a tractor manufacturer that is beginning to realize the importance of sales data in marketing its products. Its two main products are The Incisor, a tractor used in large agricultural settings, and The Caddy, a smaller tractor primarily used in landscape. The company divides its market into four geographic regions. With the aim of maximally allocating its resources, Aragon decides to investigate whether there is a relationship between the variables type of Aragon tractor sold ("The Incisor" or "The Caddy") and geographic region of the sale ("Great Lakes", "Ohio Valley", "Mid-Atlantic", or "Corn Belt"). The contingency table below summarizes sales data from 500 Aragon tractor sales. Each cell of the table contains three numbers: the first number is the observed cell frequency (); the second number is the expected cell frequency (f,) under the assumption that there is no relationship between the type of tractor sold and the geographic region of the sale; and the third number is the following value. D ( So- SE ) (Observed cell frequency - Expected cell frequency) SE Expected cell frequency The numbers labeled "Total" are totals for observed frequency. Part 1 Fill in the missing values in the contingency table. Round your expected frequencies to two or more decimal places, and round your values to three or more decimal places Send data to Excel Geographic region of the sale X ? Great Lakes Ohio Valley |Mid-Atlantic Corn Belt Total 154 75 67 120 The Incisor 81.54 113.98 416 0.525 0.318 Type of tractor 38 23 The Caddy 0 16.46 23.02 84 2 599 1.574 Total 192 98 73 137 500 Part 2 Answer the following to summarize the test of the hypothesis that there is no relationship between the type of Aragon tractor sold and the geographic region of the sale. For your test, use the 0.05 level of significance (a) Determine the type of test statistic to use. X ? Type of test statistic: (Choose one) (b) Find the value of the test statistic. (Round to two or more decimal places.) (c) Find the p-value. (Round to three or more decimal places.) (d) Can we conclude that there is a relationship between the type of Aragon tractor sold and the geographic region of the sale? Use the 0.05 level of significance. Yes