{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

1 - Statistics 144 Sample Midterm Solutions Fall Quarter...

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

Statistics 144 — Sample Midterm – Solutions Fall Quarter 2009 PROBLEM 1 Suppose a population of N = 6 units has the following values y 1 = 10, y 2 = 6, y 3 = 9, y 4 = 11, y 5 = 17 and y 6 = 14. Suppose, we take a sample of size n = 3 (a) Give the sampling distribution of the sample total. There are ( 6 3 ) = 20 different samples. t S 25 26 27 29 30 31 32 33 ¯ y 8.33 8.67 9 9.67 10 10.33 10.67 11 f ( S ) 0.05 0.05 0.05 0.05 0.10 0.05 0.05 0.10 t S 34 35 36 37 38 40 41 42 ¯ y 11.33 11.67 12 12.33 12.67 13.33 13.67 14 f ( S ) 0.10 0.05 0.05 0.10 0.05 0.05 0.05 0.05 Total: t y = 67 Mean: ¯ y U = 11 . 17 Variance: S 2 = 14 . 97 (b) Give an estimate for the population total and show that it is unbiased. Total: t y = 67 estimated by ˆ t y = 6¯ y = 6 3 t S E ( ˆ t y ) = 6 3 · E ( y ) = 6 3 ( 25 · 0 . 05 + 26 · 0 . 05 + ... + 41 · 0 . 05 + 42 · 0 . 05 ) = 67 (c) Calculate its standard error using the sampling distribution and compare it to the formula given in class. SE ( ˆ t y ) = 36 9 ( 25 2 · 0 . 05 + 26 2 · 0 . 05 + ... + 41 2 · 0 . 05 + 42 2 · 0 . 05 ) - 67 2 = 9 . 476 Formula in class SE ( ˆ t y ) = N · ( 1 - n N ) · S n = 9 . 476 PROBLEM 2 The table below gives the number of refereed publications of a sample of 50 faculty (N=807) at a university. Assume a SRS was taken. pub 0 1 2 3 4 5 6 7 8 9 10 #fac 28 4 3 4 4 2 1 0 2 1 1

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

View Full Document
(a) Calculate the mean number of publications per faculty.
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}