Answered step by step
Verified Expert Solution
Link Copied!

Question

1 Approved Answer

Let Xi,X2, . . . Xn be independent and identically distributed (lid) draws from some distribution. You wish to estimate the population median 7]. Recall

image text in transcribed
image text in transcribed
Let Xi,X2, . . . Xn be independent and identically distributed (lid) draws from some distribution. You wish to estimate the population median 7]. Recall that the median is defined so that 17(7)) : 0.5. You wish to test H0 : n S 14 vs. H1 : 7] > 14. It can be shown that an appropriate test statistic is the number of observations with a value greater than 14. In other words, let Z be our test statistic where: _ 0 Xi14 K'{1 X9141 and Z : 2:121 K- a. What is the probability that K; = 1? (use the definition of the median) (int) b. What is the distribution of your test statistic Z? Hint: it is not normal, but it is another very common distribution you have seen many times. Recall that you have iid data. (2pt) c. Intuitively explain why your rejection region will be ofthe form C = {Z 2 c}. (1pt) d. Find c for a sample size n = 6 and an o: no greater than 0.05. What is your actual significance level? (3pt) e. Given the data a: : {4, 8, 15, 16, 23, 42} calculate your test statistic, state your conclusion, and find your p-value. (3pt)

Step by Step Solution

There are 3 Steps involved in it

Step: 1

blur-text-image

Get Instant Access to Expert-Tailored Solutions

See step-by-step solutions with expert insights and AI powered tools for academic success

Step: 2

blur-text-image_2

Step: 3

blur-text-image_3

Ace Your Homework with AI

Get the answers you need in no time with our AI-driven, step-by-step assistance

Get Started

Recommended Textbook for

Calculus Single And Multivariable

Authors: Deborah Hughes Hallett, Andrew M Gleason, William G McCallum

8th Edition

1119783267, 9781119783268

More Books

Students also viewed these Mathematics questions

Question

2. Information that comes most readily to mind (availability).

Answered: 1 week ago