Page 1
Statistics 21
Problems from past midterms: midterm 2
1. (10 points) A list of numbers has an average of 51. A new list is formed by subtracting
50 from every number on the original list. The r.m.s. of the numbers on the new list is
3.0.
(a) Find the average of the new list.
(b) Find the SD of the original list.
2. (5 points) A tiny town consist of ±ve blocks. Three people live on each block, so the total
population of the town is 15. A simple random sample of ±ve people is taken from the
population. Find the chance they all live on different blocks.
3.
(10 points) A small room contains 4 rows of 5 chairs:
front of room
back of room
In (a), (b), (c) below, people enter the room one at a time, and the room is empty before
they start to come in. The ±rst person to enter is assigned at random to one of the
twenty seats in the room; the second person to enter is assigned at random to the nine
teen seats remaining; and so on.
You can leave your answers in a box looking something like:
Ans = 19
×
(17/107
×
6/94
×
15/150
×
29/780
×
3/57) + … +
more terms like that
Remember to show your reasoning, though.)
(a) Two people enter the room. Find the chance they end up sitting beside each other.
(b) Three people enter the room. Find the chance they end up in the circled seats.
(c) Five people enter the room. Find the chance three of them (no more, no less) end up
in the front row.
4. (10 points) Seventy±ve draws will be made at random, with replacement, from the box:
–3
–2
–1
1
2
3
Some of the numbers drawn will be positive, others negative. Find, approximately, the
chance the sum of all the positive numbers is bigger than 80.
5. (10 points) An educational sociologist mails a questionnaire to a simple random sample
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentPage 2
of 500 teachers taken from the 30,000 members of a state teachers association. Eighty
percent of the state’s teachers belong to the association. The questionnaire contains both
multiple choice items and openended questions. One of the openended questions asks
the teachers to describe their attitude to home schooling. When the sociologist starts
to review the returned questionnaires, he Fnds that some of the teacher’s responses to
this particular question are brief, and others are much more extensive. He puts aside,
for later analysis, the longer responses. There were 97 such responses. Of the remaining
403, he Fnds that 238 clearly favored home schooling and 165 were opposed to it. Using
this 238 out of 403, the sociologist intends to calculate a 95% conFdence interval for the
percentage of the association membership who are in favor of home schooling.
Is this calculation appropriate? If it is, explain why and Fnd the conFdence interval. If it
is not appropriate, explain why not.
This is the end of the preview.
Sign up
to
access the rest of the document.
 Fall '08
 anderes
 Statistics, Simple random sample, Household income in the United States, r.m.s.

Click to edit the document details