代做HW 7留学生、Java/c++代写、Python程序设计代做、data代写

日期：2019-04-30 10:23

Statistics: HW 7

Deadline: April 18 at 8 p.m.

Problem 1. Suppose we have n data points drawn from a N(μ, 5

2

) distribution, where

the value of μ is unknown.

(a) (1 point) Suppose we have 16 data points and that the sample mean is ˉx = 20.

Construct a precise 95% confidence interval for the μ.

(b) (1 point) Explain why the confidence interval for the mean when n = 100 is always

narrower than the confidence interval when n = 10.

(c) (1 point) What is the smallest value of n so that the 95% confidence interval for the

mean will have width less than 1.0? (Still with σ2 = 52)

Problem 2. Adult mayflies live anywhere from 30 minutes to 1 day, depending on the

species. Data for one species was collected by tracking 10 mayflies. The recorded lifespans

in hours were

17.68, 13.69, 11.22, 11.05, 13.86, 14.47, 14.50, 13.47, 10.04, 13.10

(a) (1 point) Compute a 95% confidence interval for the mean lifetime of this species of

mayfly.

(b) (1 point) What assumptions did you make in part (a)?

(c) (1 point) Compute a 95% confidence interval for the standard deviation of distribution

of the lifetime of a mayfly.

(d) (1 point) Based on the sample variance of this data estimate the number of data

points you would need to make the width of the 95% confidence interval for the

mean less than or equal to 1 hour.

(e) (1 point) Is the value of n in part (d) guaranteed to be sufficient? Explain your

reasoning.

Problem 3. Finish the t-test task from the practice:

(a) (4 points) Build the distribution of p-values when H0 is true

(b) (8 points) Build the distribution of p-values when H0 is false. Try to decrease the

sample size, while holding the mean the same. Try to increase the mean while

holding the sample size the same. Explain your results.

(c) (4 points) Build the distribution of p-values when xi ～ Exp(1) and sample size

n = 5. Explain your results.

Problem 4. Consider the z-test (slides 35–37):

(a) (4 points) Build the distribution of p-values when H0 is true. Please consider different

distributions.

(b) (8 points) Build the distribution of p-values when H0 is false. Please consider different

distributions. Try to decrease the sample size, while holding the mean the

same. Try to increase the mean while holding the sample size the same. Explain

your results.

(c) (4 points) Build the distribution of p-values when xi ～ Cauchy and sample size

n = 1000. Explain your results.