A machine is designed to mix nuts so that 40% of the resulting product will consist of pecans, 10% will be cashews, 25% will be almonds and 25% will be peanuts. A sample of 180 nuts is taken and it is found that 67 are pecans, 30 are cashews, 40 are almonds and 43 are peanuts. Do the data suggest that the machine is mixing nuts in conformity with its design? Test at αα = 0.01.
Report all answers to three decimal places.
(a). Complete the table of observed counts:
Pecans | Cashews | Almonds | Peanuts |
67 | 30 | 43 |
(b). Complete the table of expected counts:
Pecans | Cashews | Almonds | Peanuts |
72 | 45 | 45 |
(c). Complete the table of contributions to the chi square test statistic:
Pecans | Cashews | Almonds | Peanuts |
8 | 0.556 | 0.089 |
(d). Using your answers from part (c), the test-statistic is
(e). The degrees of freedom are
(f). The critical value is
(g). You decide to Select an answer reject fail to reject the null hypothesis and conclude that the machine Select an answer is is not mixing nuts in conformity with its design.
A machine is designed to mix nuts so that 40% of the resulting product will consist...