1. Art, nuts! A company claims that each batch of its deluxe muted nuts contains Pg 52" o cashews= 2'.\" o almornds= 13% macadamia nuts= and 8'.\" 0 Brazil nuts. To test this claim, a quality-control inspector takes a random sample of 150 nuts 'om the latest batch. The table displays the sample data. Type of nut Cashew Almond Macadamia Brazrl Count 83 19 20 18 a. State appropriate hypotheses for performing a test of the company's claim. b. Calculate the expected count for each type of nut- c. Calculate the value of the chi-square test statistic. 9. Handling Froot Loops Kellogg's Froot Loops cereal comes in six colors: PG orange. yellow. purple. red. lslue= and green. C harise randomly selected 120 loops 1" H} and noted the color of each. Here are her data: Color Orange Yellow Purple Red Blue Green Count 23 31 lo 25 14 16 Do these data provide convincing evidence at the 5 to signicance level that Kellogg's Froot Loops do not contain an equal proportion of each color? 14. Seagulls by the seashore Do seagulls show a preference for where they land? To answer this question, biologists conducted a study in an enclosed outdoor space with a piece of shore whose area was made up of 56% sand, 29% mud, and 15% rocks. The biologists chose 200 seagulls at random. Each seagull was released into the outdoor space on its own and observed until it landed somewhere on the piece of shore. In all= 138 seagulls landed on the sand= 61 landed in the inud= and ll landed on the rocks. a- Do these data provide convincing evidence that seagulls show a preference for where they land?J b. Relative to the proportion of each ground type on the shore= which type of ground do the seagulls seem to prefer the most? The least