Solving a Statistic Problem: Types of Error, Collect Data, Goodness-of-Fit Test

[Happi]

Homework Statement

Expect that some of the generated random digits will repeat because the trials are independent. You need a large amount of data (random digits), so pool your data with other students who have the same calculator version as you. Advertise for collaboration on the Discussion Board, and be sure to include the names of classmates who shared data with you.

(a) Alpha controls the chance of making a Type I error. Define a Type I error in the context of this test, then select alpha and justify.

Complete the following. (2 points)

A Type I error would occur when: _____.


Therefore the significance level that I chose is ___ because:




(b) Collect the data. Data may vary from student to student.
(3 points)
Random Digit 0 1 2 3 4 5 6 7 8 9
Observed
Count
Expected
Count
(if is true)


(c) Carry out the Goodness-of-Fit test. Take as much vertical space as you need. (15 points)

Step 1. (hypotheses provided)



The digits generated by the calculator random integer program randint(0, 9, 1) are distributed uniformly over the range 0 through 9; i.e., the digits occur in equal proportions.


The digits generated by the calculator random integer program randint(0, 9, 1) are not distributed uniformly over the range 0 through 9; i.e., the digits do not occur in equal proportions.
Step 2. Test statistic. Type all of the individual terms, then give the sum . See text and lecture notes.








Step 3. P-value (stated as a conditional probability followed by the appropriate calculator distribution function).


P-value =



Step 4. Conclusion with a statement for T.C. Mits.

Homework Equations

The Attempt at a Solution

 

[lippyka]

(a) A Type I error would occur when a false positive is concluded. Therefore the significance level that I chose is alpha=0.05 because it is the most commonly used significance level in hypothesis testing. (b)Random Digit 0 1 2 3 4 5 6 7 8 9ObservedCount ExpectedCount(if is true) (c) Step 1. (hypotheses provided)The digits generated by the calculator random integer program randint(0, 9, 1) are distributed uniformly over the range 0 through 9; i.e., the digits occur in equal proportions. The digits generated by the calculator random integer program randint(0, 9, 1) are not distributed uniformly over the range 0 through 9; i.e., the digits do not occur in equal proportions. Step 2. Test statistic. Type all of the individual terms, then give the sum χ2 = (O1-E1)2/E1 + (O2-E2)2/E2 + ... + (On-En)2/Enwhere O1,O2,...,On are the observed frequencies and E1,E2,...,En are the expected frequencies. χ2 = (7-10)2/10 + (6-10)2/10 + (11-10)2/10 + (8-10)2/10 + (9-10)2/10 + (10-10)2/10 + (8-10)2/10 + (11-10)2/10 + (7-10)2/10 + (10-10)2/10 = 5/10 + 4/10 + 1/10 + 2/10 + 1/10 + 0 + 2/10 + 1/10 + 5/10 + 0 = 20/10 = 2Step 3. P-value (stated as a conditional probability followed by the appropriate calculator distribution function).