Busy. Please wait.

show password
Forgot Password?

Don't have an account?  Sign up 

Username is available taken
show password


Make sure to remember your password. If you forget it there is no way for StudyStack to send you a reset link. You would need to create a new account.

By signing up, I agree to StudyStack's Terms of Service and Privacy Policy.

Already a StudyStack user? Log In

Reset Password
Enter the associated with your account, and we'll email you a link to reset your password.

Remove ads
Don't know
remaining cards
To flip the current card, click it or press the Spacebar key.  To move the current card to one of the three colored boxes, click on the box.  You may also press the UP ARROW key to move the card to the "Know" box, the DOWN ARROW key to move the card to the "Don't know" box, or the RIGHT ARROW key to move the card to the Remaining box.  You may also click on the card displayed in any of the three boxes to bring that card back to the center.

Pass complete!

"Know" box contains:
Time elapsed:
restart all cards

Embed Code - If you would like this activity on your web page, copy the script below and paste it into your web page.

  Normal Size     Small Size show me how


Goodness-of-Fit Test

What symbol is used to represent the “chi-square” random variable? The symbol used to represent the “chi-square” random variable is “χ^2”.
Is the “chi-square” distribution always symmetric like the z-distribution and t-distribution? No. The “chi-square” distribution is not generally symmetric.
What determines the shape of the chi-square distribution? The shape of the chi-square distribution depends on the degrees of freedom, just like Student’s t-distribution.
Will the chi-square distribution ever be roughly symmetric? Yes. As the number of degrees of freedom increases, the chi-square distribution becomes more nearly symmetric.
Will the values of the chi-square distribution ever be negative? No. The values of “χ^2” are nonnegative, i.e., the values of “χ^2”are greater than or equal to 0.
What is a “goodness-of-fit” test? A “goodness-of-fit” test is an inferential procedure used to determine whether a frequency distribution follows a specific (“claimed”) distribution. The chi-square distribution is used in conducting the goodness-of-fit test.
How are the hypotheses for the goodness-of-fit test specified? The Null and Alternative hypotheses are setup as follows: H0: The random variable follows a certain distribution H1: The random variable does “not” follow a certain distribution
Based on the way the alternative hypothesis is specified, is the goodness-of-fit test a two-tailed test? No. While the wording might lead you to believe that the goodness-of-fit test is a two-tailed test, it is, in fact, ALWAYS A RIGHT TAILED TEST.
How is the “test statistic” for the goodness-of-fit test calculated? The “test statistic” = “χ^2”. = Σ[(Oi – Ei)^2/Ei], where the Oi values are the OBSERVED counts from the sample and the Ei values are the EXPECTED counts (the counts expected if the claimed distribution were true); i = 1,...,k.
Under the “classical approach”, how to we decide whether to reject or not reject the null hypothesis? Under the classical approach, we would determine the critical chi-square value. If the test statistic is greater than the critical chi-square value we REJECT the null hypothesis, otherwise we DO NOT REJECT the null hypothesis.
How is the critical chi-square value calculated? Using Tables, you would find appropriate critical chi-square value based on k-1 degrees of freedom, where “k” is the number of data categories, and “α”, the level of significance. Some calculators have a program for the INVCHI function that may be used.
Uisng Tables, you would find appropriate critical chi-square value based on k-1 degrees of freedom, where “k” is the number of data categories, and “α”, the level of significance. Some calculators have a program for the INVCHI function that may be used. Under the “p-value approach”, calculate the probability that a randomly selected value from the chi-square distribution is greater than the “test statistic”. As always, if this p-value is LESS THAN α, REJECT the null hypothesis; otherwise, DO NOT REJECT.
How is the “p- value calculated”? If you are using a TI-83/84, you would use 2nd VARS and choose χ^2cdf. The format is: χ^2cdf(lower bound, upper bound, df), where: lower bound = the test statistic; upper bound = 1E99; “df”, degrees of freedom = k – 1.
As an example, calculate the p-value if the calculated value of the test statistic is 6.605 and there are k = 5 categories of data. The format to compute the p-value is: χ^2cdf(6.605, 1E99, 4) = 0.1583 Note the degrees of freedom: k – 1 = 5 – 1 = 4.
Is there a function in the TI-83/84 that will calculate all the values necessary to perform the goodness-of-fit test? The TI-84 does have such a function, but the Ti-83 does not. Enter the OBSERVED values in L1 and the EXPECTED values in L2. In the TI-84, use STAT ==>TESTS ==> D: χ^2GOF – Test.
Created by: wgriffin410