This module introduces the contingency table as a way of determining conditional probabilities.
A
contingency table provides a way of portraying data that can facilitate calculating probabilities. The table helps in determining conditional probabilities quite easily. The table displays sample values in relation to two different variables that may be dependent or contingent on one another. Later on, we will use contingency tables again, but in another manner.
Contingincy tables provide a way of portraying data that can facilitate calculating probabilities.
Suppose a study of speeding violations and drivers who use car phones produced the following fictional data:
Speeding violation
in the last year
No speeding violation
in the last year
Total
Car phone user
25
280
305
Not a car phone user
45
405
450
Total
70
685
755
The total number of people in the sample is 755. The row totals are 305 and 450. The column totals are 70 and 685. Notice that
and
.
Calculate the following probabilities using the table
Find the probability that a person is male given that the person prefers hiking near lakes and streams. Let
= being male and let
= prefers hiking near lakes and streams.
What word tells you this is a conditional?
Fill in the blanks and calculate the probability:
.
Is the sample space for this problem all 100 hikers? If not, what is it?
The word 'given' tells you that this is a conditional.
Muddy Mouse lives in a cage with 3 doors. If Muddy goes out the first door, the probability that he gets caught by Alissa the cat is
and the probability he is not caught is
. If he goes out the second door, the probability he gets caught by Alissa is
and the probability he is not caught is
. The probability that Alissa catches Muddy coming out of the third door is
and the probability she does not catch Muddy is
. It is equally likely that Muddy will choose any of the three doors so the probability of choosing each door is
.
Door choice
Caught or Not
Door One
Door Two
Door Three
Total
Caught
____
Not Caught
____
Total
____
____
____
1
The first entry
is
.
The entry
is
.
Verify the remaining entries.
Complete the probability contingency table. Calculate the entries for the totals. Verify that the lower-right corner entry is 1.
Step 1: Find the mean. To find the mean, add up all the scores, then divide them by the number of scores. ...
Step 2: Find each score's deviation from the mean. ...
Step 3: Square each deviation from the mean. ...
Step 4: Find the sum of squares. ...
Step 5: Divide the sum of squares by n – 1 or N.
The sample of 16 students is taken. The average age in the sample was 22 years with astandard deviation of 6 years. Construct a 95% confidence interval for the age of the population.
Bhartdarshan' is an internet-based travel agency wherein customer can see videos of the cities they plant to visit. The number of hits daily is a normally distributed random variable with a mean of 10,000 and a standard deviation of 2,400
a. what is the probability of getting more than 12,000 hits?
b. what is the probability of getting fewer than 9,000 hits?
Bhartdarshan'is an internet-based travel agency wherein customer can see videos of the cities they plan to visit. The number of hits daily is a normally distributed random variable with a mean of 10,000 and a standard deviation of 2,400.
a. What is the probability of getting more than 12,000 hits