Question

only need help with the calculations

In order to receive credit for the homework, you must show all steps for doing a chi square test of independence. These steps include: null and alternative hypothesis); critical value; calculations (show work); reject or accept H; results statement using no relationship or a relationship.

Answer 1

The null and alternative hypothesis can be stated as: Null Hypothesis: The relationship between drinking coffee and age is independent and follows the chi-squared distribution. Alternative Hypothesis: The relationship between drinking coffee and age is not independent and does not follows the chi-squared distribution. The totals of each row and column and grand total is shown in the table below: Low 18 Moderate 10 Column and Row Totals High 12 Row Totals 21-31 31-40 41-50 >50 110 13 18 Column Totals 45 152 (Grand Total To find the chi-square test statistic, first we need to find the expected frequency for each of the observed frequency E(21-31,Low) - Total of 21-31% Total of Low Grand Total 46 x 45 152 = 13.62

Similarly, all the expected frequencies are calculated which is shown in the table below: Row Totals 21-31 31-40 41-50 > 50 Low 18 (13.62) (1.41) 18 (1362) 11.41 (15.10) [2.46] 5 7.99) (1.12) 3 (82) (2.681 Moderate 110 (15.74) 10.00) 110 (1574) 15 (17.45) 10.34] 12 (9.24) 10.83] 1 (0.58) [0.03] Results High 12 (16.84) [130] 27 (18.45) (3.98] 10 (0.77) 10.01] 16 (10.13) (1.881 1 Column Totals 45 52 55 152 (Grand Total) The chi-square test can be obtained as: r=(0-E) X = E E (18-13.62)2 (9-15.10)2 13.62 * 15. 10 = 15.82 9 (10-9.77) .77 (6-10.13)? 10.13

The degrees of freedom for the critical value is, df =(r-1)(c-1) =(4-1)(3-1) = 3x2 = 6 The level of significance is a = 0.05. In the chi-square distribution table, locate 6 in degrees of freedom column and xãos in level of significance row. The intersecting value of row and column is 12.59. The critical value is, X5.0.03 = 12.59. The obtained p-value is 0.0147 which is less than the level of significance. So, the null hypothesis is rejected. Therefore, it can be concluded that there is a relationship between drinking coffee and age.