Question

In: Math

Use the following information to answer the next questions: A five-sided die is rolled 100 times....

Use the following information to answer the next questions: A five-sided die is rolled 100 times. Conduct a hypothesis test to determine if the die is fair. Use a 5% level of significance.
Observed Rolls: One=10; Two=29; Three=16, Four=15, Five=30
Expected Rolls: All the categories of rolls are the same

What test are you running?

What is the observed values of one for the rolled die?

What is the observed values of two for the rolled die?

What is the observed values of three for the rolled die?

What is the observed values of four for the rolled die?

What is the observed values of five for the rolled die?

What is the expected values of one,two,three,four,five for the rolled die?

What are the degrees of freedom?

What is the null hypothesis?

What is the alternative hypothesis?

What is the test statistic? Use one decimal place.

What is the p-value? Use three decimal places.

What is your conclusion based on the p-value and the level of significance?

At the 5% significance level, what can you conclude?

Solutions

Expert Solution

What test are you running?: chi square goodness of fit:

observed values of one for the rolled die=10

observed values of two for the rolled die=29

observed values of three for the rolled die=16

observed values of four for the rolled die=15

observed values of five for the rolled die=30

expected values of one,two,three,four,five for the rolled die =np =100*0.2 =20

degree of freedom =categories-1= 4

  null hypothesis: Ho:die is fair or all numbers appear with equal proportion

Alternate hypothesis: Ho:die is biased or all numbers does not appear with equal proportion

applying chi square goodness of fit test:  
           relative observed Expected residual Chi square likelihood ratio
category frequency(p) Oi Ei=total*p R2i=(Oi-Ei)/√Ei R2i=(Oi-Ei)2/Ei G2 =2*Oi*ln(Oi/Ei)
1 0.200 10.000 20.00 -2.24 5.000 -13.8629
2 0.200 29.000 20.00 2.01 4.050 21.5507
3 0.200 16.000 20.00 -0.89 0.800 -7.1406
4 0.200 15.000 20.00 -1.12 1.250 -8.6305
5 0.200 30.000 20.00 2.24 5.000 24.3279
total 1.000 100 100 16.1000 16.2446
test statistic X2 = 16.1000
p value = 0.003
since test statistic falls in rejection region we reject null hypothesis
we have sufficient evidence to conclude that,die is biased

milcah answered 9 months ago
Next > < Previous

Related Solutions

A six sided die is rolled 4 times. The number of 2's rolled is counted as...
A six sided die is rolled 4 times. The number of 2's rolled is counted as a success. Construct a probability distribution for the random variable. # of 2's P(X) Would this be considered a binomial random variable?    What is the probability that you will roll a die 4 times and get a 2 only once? d) Is it unusual to get no 2s when rolling a die 4 times? Why or why not? Use probabilities to explain.
A six sided die is rolled 4 times. The number of 2's rolled is counted as...
A six sided die is rolled 4 times. The number of 2's rolled is counted as a success. Construct a probability distribution for the random variable. # of 2's P(X) Would this be considered a binomial random variable?    What is the probability that you will roll a die 4 times and get a 2 only once?       d Is it unusual to get no 2s when rolling a die 4 times? Why or why not? Use probabilities to explain.
Suppose a red six-sided die, a blue six-sided die, and a yellow six-sided die are rolled....
Suppose a red six-sided die, a blue six-sided die, and a yellow six-sided die are rolled. Let - X1 be the random variable which is 1 if the numbers rolled on the blue die and the yellow die are the same and 0 otherwise; - X2 be the random variable which is 1 if the numbers rolled on the red die and the yellow die are the same and 0 otherwise; - X3 be the random variable which is 1...
Suppose a 6-sided die and a 7-sided die are rolled. What is the probability of getting...
Suppose a 6-sided die and a 7-sided die are rolled. What is the probability of getting sum less than or equal to 5 for the first time on the 4th roll? Show your work to receive credit.
A die is rolled 100 times. The total number of spots is 368 instead of the...
A die is rolled 100 times. The total number of spots is 368 instead of the expected 350. Can this be explained as a chance variation, or is the die loaded? A die is rolled 1000 times. The total number of spots is 3680 instead of the expected 3500. Can this be explained as a chance variation, or is the die loaded?
Example 4: A fair six-sided die is rolled six times. If the face numbered k is...
Example 4: A fair six-sided die is rolled six times. If the face numbered k is the outcome on roll k for k = 1, 2, 3, 4, 5, 6 we say that a match has occurred. The experiment is called a success if at least one match occurs during the six trials. Otherwise, the experiment is called a failure. The outcome space is O = {success, failure}. Let event A = {success}. Which value has P(A)? **This question has...
a fair 6-sided die is rolled three times. What is the probability that all three rolls...
a fair 6-sided die is rolled three times. What is the probability that all three rolls are 2? Round the answer to four decimal places
A regular six-sided die and a regular eight-sided die are rolled to find the sum. Determine...
A regular six-sided die and a regular eight-sided die are rolled to find the sum. Determine the probability distribution for the sum of the two dice. Create a frequency histogram for the probability distribution and determine the expected sum of the two dice.
Use the following information to answer the next five questions: On March 1st, Apple Inc. issued...
Use the following information to answer the next five questions: On March 1st, Apple Inc. issued 1,000 shares of $3 par value stock for a selling price of $10 per share. On May 1st, Apple Inc. reacquired 100 of the 1000 shares issued on March 1st for $15 per share. On June 1st, Apple reissued 100 shares for $20 per share. On June 10th, Apple declared a $1 per share dividend On June 12th, Apple paid the dividend that it...
Rolling a fair six-sided die five times could result in the following sample of n =...
Rolling a fair six-sided die five times could result in the following sample of n = 5 observations: What are the mean, variance, and standard deviation?
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT