Question

A pumpkin farmer weighed a simple random sample of size n = 20 pumpkins, with these results: 9.6, 8.8, 5.1, 9.7, 9.1, 8.9, 8, 9.2, 2.7, 9.1, 8.5, 7.3, 9.3, 9.6, 4.1, 9.9, 7.6, 9, 7.2, 8.5

(a) Create a QQ plot of the weights. Do you think it is reasonable to assume that the population distribution is normal? Explain your answer.

(b) Regardless of your answer to (a), use R to perform the bootstrap with 2000 resamplings to create a 90% confidence interval for μ. (Show your R code and its output.)

(c) Suppose you want to know whether the true mean pumpkin weight for this pumpkin farmer’s patch is greater than 7.2. Conduct a bootstrap hypothesis test with 2000 resamplings at a significance level α = 0.05.

(d) Conduct a hypothesis test at level α = 0.05 to see whether we can assert the data are strong evidence the true median weight for this pumpkin farmer’s patch is greater than 7.2.

Answer 1

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