Suppose e managers collect a random sample of size 51 from their field this year to test the hypotheses : $H_o : \\mu = 31$ versus $H_a : \\mu \ e 31$ at a 10 \\% significance level . They still believe it is reasonable to assume the distribution of weights for the pineapples is approximately normal , but they are not going to assume they know $ \\sigma $. The collected pineapple weights can be found in the " Pineapples . csv " file on Canvas f . Evaluate whether the assumptions of the t test are reasonably met . > g. Compute a t test t statistic and p value and draw a conclusion for the hypothesis test $H_o : \\mu = 31$ versus $H_a : \\mu \ e 31$ at a 10 \\% level . ( I would recommend you do this "by hand " and also with an R function to check your work ) > h. Perform a bootstrap hypothesis test of $H_o : \\mu = 31$ versus $H_a : \\mu \ e 31 $ at the 10 \\% level > i. Explain why using the t, z, or bootstrap tools are all reasonable in this scenario * * Exercise 2* * The p- value for a two - sided t test of the hypotheses $HO : \\mu = 15 $ , $HA : \\mu ne 15 $ is 0. 03 . > a. Does the 99 \\% [ two - sided ] confidence interval for $\\mu$ using this same sample include 15 ? Why or why not ? > b. Does the 95 \\% [ two - sided ] confidence interval for $\\mu$ using this same sample include 15 ? Why or why not ? * * Exercise 3* * Permethrin is a chemical that is recommended as a way of controlling insects . One study on the effectiveness of Permethrin on plant leaves inspected 96 plants and reported a 90 \\% t confidence interval of : (6.132 , 8.268 ) for the average number of insects on plants treated with Permethrin . What would be the p value