{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Exam1_4502_sol - STA4502 Section 2906 EXAM 1 Solutions 1...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
STA4502 Section 2906 EXAM 1. Solutions 1. Below are recorded the white blood cell counts for a sample of 6 adult males with leukemia (recorded in thousands of cells). 19.3 32.0 1.8 43.0 14.1 1.4 Making no assumptions about the distribution of white cell counts in this population, find a point estimate of the median white blood cell count for the population of adult male with leukemia. Also, find roughly 80% confidence intervals for the population median cell count and interpret it. (10 pts) ˆ θ 0 . 5 = 14 . 1 + 19 . 3 2 = 16 . 7 From R , a roughly 80% confidence interval for the population median is given by [ X (2) , X (5) ) = [1 . 8 , 32 . 0) and the achieve confidence level is 4 summationdisplay k =2 parenleftbigg 6 k parenrightbigg parenleftbigg 1 2 parenrightbigg 6 = 0 . 78125 . We are 78 . 13% confident that the median white blood cell count for the population of adult male with leukemia falls in the interval [1 . 8 , 32 . 0). 2. Suppose X 1 , . . . , X 10 iid F . Let θ 0 . 5 = median of F . Find Pr bracketleftbig X (2) θ 0 . 5 < X (9) bracketrightbig . (5 pts) Pr bracketleftbig X (2) θ 0 . 5 < X (9) bracketrightbig = 8 summationdisplay k =2 parenleftbigg 10 k parenrightbigg parenleftbigg 1 2 parenrightbigg 10 0 . 9785 3. Describe the general principle that related a 90% confidence interval to a test of hypothesis. (5 pts) The 90% confidence interval consists of all the θ 0 values such that the test of H 0 : θ = θ 0 H a : θ negationslash = θ 0 would not reject H 0 in a two-sided α = 0 . 1 test of hypothesis.
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
$435 -$1,735 $822 $572 -$308 $116 -$786 $51 4. The Internal Revenue Service takes a sample of tax returns and records the refund amount requested from the government ( A negative refund means that person owed the government.) A sample of eight returns showed the refunds below: Does this data indicate that the population median tax refund amount is positive? Make no assumption about the nature of the underlying population in conducting this test. Find the p value . (10 pts) H 0 : θ 0 . 5 = 0 H a : θ 0 . 5 > 0 Under H 0 , p = Pr ( X > 0) = 0 . 5. Thus, H 0 : p = 0 . 5 H a : p > 0 . 5 Test stat B = 8 summationdisplay i =1 I ( X i > 0) Under H 0 , B Binomial( n = 8 , p = 0 . 5). Therefore, p value = Pr ( B B obs ) = Pr ( B
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}