Hypothesis Testing of Two Means and Two Proportions: Review
1.5
2008/06/17 09:32:02 GMT-5
2008/08/15 14:56:27.585 GMT-5
Barbara
Illowsky
illowskybarbara@deanza.edu
Susan
Dean
deansusan@deanza.edu
Connexions
cnx@cnx.org
elementary
statistics
The next three questions refer to the following information:
In a survey at Kirkwood Ski Resort the following information was recorded:
Sport Participation by Age
0 – 10
11 - 20
21 - 40
40+
Ski
10
12
30
8
Snowboard
6
17
12
5
Suppose that one person from of the above was randomly selected.
Find the probability that the person was a skier or was age 11 – 20.
77
100
size 12{ { { size 8{"77"} } over { size 8{"100"} } } } {}
Find the probability that the person was a snowboarder given he/she was age 21 – 40.
12
42
size 12{ { { size 8{"12"} } over { size 8{"42"} } } } {}
Explain which of the following are true and which are false.
- aSport and Age are independent events.
- bSki and age 11 – 20 are mutually exclusive events.
- c
P
(
Ski
and
age
21
−
40
)
<
P
(
Ski
∣
age
21
−
40
)
size 12{P \( ital "Ski"+ ital "age""21" - "40" \) <P \( ital "Ski" \lline ital "age""21" - "40" \) } {}
- d
P
(
Snowboard
orage
0
−
10
)
<
P
(
Snowboard
∣
age
0
−
10
)
size 12{P \( ital "Snowboardorage"0 - "10" \) <P \( ital "Snowboard" \lline ital "age"0 - "10" \) } {}
- aFalse
- bFalse
- cTrue
- dFalse
The average length of time a person with a broken leg wears a cast is approximately 6 weeks. The standard deviation is about 3 weeks. Thirty people who had recently healed from broken legs were interviewed. State the distribution that most accurately reflects total time to heal for the thirty people.
N
(
180
,
16
.
43
)
size 12{N \( "180","16" "." "43" \) } {}
The distribution for
X size 12{X} {} is Uniform. What can we say for certain about the distribution for
X¯ size 12{ {overline {X}} } {} when
n=1 size 12{n=1} {}?
- AThe distribution for
X¯ size 12{ {overline {X}} } {} is still Uniform with the same mean and standard dev. as the distribution for
X size 12{X} {}.
- BThe distribution for
X¯ size 12{ {overline {X}} } {}is Normal with the different mean and a different standard deviation as the distribution for
X size 12{X} {}.
- CThe distribution for
X¯ size 12{ {overline {X}} } {} is Normal with the same mean but a larger standard deviation than the distribution for
X size 12{X} {}.
- DThe distribution for
X¯ size 12{ {overline {X}} } {} is Normal with the same mean but a smaller standard deviation than the distribution for
X size 12{X} {}.
A
The distribution for X size 12{X} {} is uniform. What can we say for certain about the distribution for ∑X size 12{ Sum {X} } {} when n=50 size 12{n=50} {}?
- AThe distribution for
∑X size 12{ Sum {X} } {}is still uniform with the same mean and standard deviation as the distribution for
X size 12{X} {}.
- BThe distribution for
∑X size 12{ Sum {X} } {} is Normal with the same mean but a larger standard deviation as the distribution for
X size 12{X} {}.
- CThe distribution for
∑X size 12{ Sum {X} } {} is Normal with a larger mean and a larger standard deviation than the distribution for
X size 12{X} {}.
- DThe distribution for
∑X size 12{ Sum {X} } {} is Normal with the same mean but a smaller standard deviation than the distribution for
X size 12{X} {}.
C
The next three questions refer to the following information:
A group of students measured the lengths of all the carrots in a five-pound bag of baby carrots. They calculated the average length of baby carrots to be 2.0 inches with a standard deviation of 0.25 inches. Suppose we randomly survey 16 five-pound bags of baby carrots.
State the approximate distribution for
X¯ size 12{ {overline {X}} } {}, the distribution for the average lengths of baby carrots in 16 five-pound bags.
X¯~ size 12{ {overline {X}} "~" } {}
N
( 2
,
.25
16
)
size 12{N \( { { size 8{2 "." "25"} } over { size 8{ sqrt {"16"} } } } \) } {}
Explain why we cannot find the probability that one individual randomly chosen carrot is greater than 2.25 inches.
Find the probability that
X¯ size 12{ {overline {X}} } {} is between 2 and 2.25 inches.
0.5000
The next three questions refer to the following information:
At the beginning of the term, the amount of time a student waits in line at the campus store is normally distributed with a mean of 5 minutes and a standard deviation of 2 minutes.
Find the 90th percentile of waiting time in minutes.
7.6
Find the median waiting time for one student.
5
Find the probability that the average waiting time for 40 students is at least 4.5 minutes.
0.9431