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Ryan, Engineer

Category: Math Homework

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Experience: B.S. in Civil Engineering

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Please explain all steps and show workPart I. Consider the

Customer Question

Please explain all steps and show work Part I. Consider the hypothesis test given by H₀: P=0.5 H₁: P <0.5 In a random sample of 100 subjects, the sample proportion is found to be p ̂ =0.47 .

(a) Determine the test statistic. Show all work

(b) Determine the p-value for this test. Show work

(c) Is there sufficient evidence to justify the rejection of H₀ at the α = 0.01 level? Explain answer.

Part 2: Rabbits like to eat the cucumbers in Mimi’s garden. There are 10 cucumbers in her garden which will be ready to harvest in about 10 days. Based on her experience, the probability of a cucumber being eaten by the rabbits before harvest is 0.60. Show all work

(a) Let X be the number of cucumbers that Mimi harvests (that is, the number of cucumbers not eaten by rabbits). As we know, the distribution of X is a binomial probability distribution. What is the number of trials (n), probability of successes (p) and probability of failures (q), respectively?

(b) Find the probability that Mimi harvests at least 2 of the 10 cucumbers. (round the answer to 3 decimal places)