Download STATISTICS AND THE TI-83 Sanchez 98-1

STATISTICS AND THE TI-83
Lesson 15
Sampling
or 
To display the MATH PROB menu, press MATH
1. rand: generates and returns one random numbers ≥0 and ≤1.
. rand(n): generates and returns n random numbers ≥0 and ≤1.
Exercise 1. Store 10 random numbers ≥0 and ≤1 on a list L1.

MATH
PROB 1 rand(10)
STO 
2nd L1
ENTER
answer: you should obtain 10 random numbers
Note. An expression can be included in to generate numbers ≥1.
The expression rand(n)*(a-b)+b will give n random numbers >b and <a
Exercise 2: Store 8 random numbers on a list L2. Numbers should be ≥1 and <6, rounded to
2 decimal places.

MODE FLOAT

MATH

ENTER
 2 ENTER 2nd QUIT
PROB 1 rand(8)*5+1
STO 
2nd L2
(you get a list of 8 numbers ≥1 and <6)
n STO  rand generates a different number sequence.
To generate a different random number sequence, store any nonzero seed value to rand. To
restore the factory-set seed value, store 0 to rand or reset the defaults.
EXERCISE 3. Store 10 random numbers on a list L3. Numbers should be ≥0 and <20, round
answers to 1 decimal place.

MODE FLOAT  1

MATH

STO 2nd L3
ENTER 2nd QUIT
PROB 1 rand(10)*20
ENTER
Exercise 4: Store 15 random numbers on a list L1. Numbers should be ≥3 and <25, rounded
to 2 decimal places.

MODE FLOAT

MATH

ENTER (you get a list of 15 numbers)
 2 ENTER 2nd QUIT
PROB 1 rand(15)*22+3
STO 
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2nd L1
Exercise 5: Store 50 random numbers on a list L2. Numbers should be
≥7.3 and
<42.8, rounded to 2 decimal places. Find the descriptive measures of the values in L 2.

MODE FLOAT

MATH

STO  2nd L2 ENTER

STAT
 2 ENTER 2nd QUIT
PROB 1 rand(50)*35.5+7.3
 CALC
ENTER (you get a list of 50 numbers)
1 1-Var Stats 2nd L2 ENTER
5. RndInt(lower, upper, number): returns a list of n integers within
two bounds, inclusive.
MATH
PRB 5 randInt(L, U, n)
Exercise 6 : store 10 random integers from 4 to 13 in L 3
PRB 5 randInt(4, 13, 10) ENTER STO  2nd L3

MATH

ENTER
6. randNorm(mean, stdv, n): returns a sample of size n selected from a
normal population with a given mean and standard deviation.
MATH
PRB 6 randNorm(  ,  , n )
Exercise 7: store 10 random numbers from a normal population
with mean 20 and standard deviation 2.

MATH
ENTER STO  2nd L4 ENTER
PRB 6 randNorm (20, 2, 10)
Compute the descriptive measures of the sample

STAT
 CALC
1 1-Var Stats 2nd L4 ENTER
7. randBin(number of trials, probability of success for each trial, Number of simulations)
MATH
PRB
7 randBin (n, p, # of successes)
Exercise 8: find the number of heads in 6 tosses of a coin. Repeat the experiment 20 times.
Use a binomial simulation.

MATH
PRB
7 randBin (6, .5, 20)
ENTER
STO 
2nd L5
ENTER
Find the descriptive measures of the 20 observations. How close is the mean to np=6(.5)=3
and the standard deviation to

STAT
 CALC
6(.5)(.5) =1.224744871? Observe.
1 1-Var Stats 2nd L5
ENTER
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In the following exercise answers will vary from my answers because of randomness.
Exercise 9: Repeat the experiment of problem 8, 200 times. Use a binomial simulation.

MATH
PRB
7 randBin (6, .5, 200)
STO 
ENTER
2nd L6
ENTER
a) Find the descriptive measures of the 200 observations. How close is the mean to np=6(.5)=3
and the standard deviation to

STAT
 CALC
6(.5)(.5) =1.224744871?, observe.
1 1-Var Stats 2nd L6
ENTER
b) Find the distribution of values for the number of heads in the sample of 200 simulations.

Y= (delete all existing plots and functions)

2nd STAT PLOT 1

select ON
histogram
XList: L6

WINDOW
Xmin=-1
Xmax=8

TRACE (obtain frequencies by tracing)
Freq: 1
Ymin=-1
Ymax=100
GRAPH
X
0
1
2
3
4
5
6
F
2
23
43
68
45
16
3
c) Find the probability that the number of heads is exactly 4. Check by using the binomial
distribution.

45  200 =.225

2nd DISTR 0 binompdf(6, .5, 4) ENTER
answer: .234376
d) Find the probability that the number of heads is less than or equal to 4. Check by using the
binomial distribution.

181  200 =.905

2nd DISTR ALPHA A binompdf(6, .5, 4) ENTER
answer: .890625
Exercise 10: For a binomial with n=12, p=.4, the mean = np = 4.8 and the standard deviation is
np(1  p)  12(.4)(.6)  1.70
Use 100 simulations to check those results. Use the STAT CALC

MATH
PRB 7 randBin (12, .4, 100)
STO 

STAT
CALC 1 1-Var Stats 2nd L6
ENTER
Observe the results.
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2nd L6 ENTER