Exam 14: Goodness-Of-Fit Tests and Categorical Data Analysis

The area to the right of 4.93 under the 2 degrees of freedom chi-squared curve is __________.

If Z is a standard normal random variable; that is $Z \square N ( 0,1 )$ , then $Z ^ { 2 }$ has a __________ distribution with degrees of freedom $v$ = __________.

The chi-squared test for homogeneity can safely be applied as long as the estimated expected count $\hat { e } _ { y }$ is at least __________ for all cells.

It is true that the more the sample correlation coefficient r deviates from __________, the less the normal probability plot resembles a straight line.

Which of the following statements are true?

If the computed value of the chi-squared test statistic is $\chi ^ { 2 }$ =2.83, and the test has 2 degrees of freedom, then the null hypothesis $H _ { 0 }$ is __________ at .05 level of significance.

The accompanying data refers to leaf marks found on white clover samples selected from both long-grass areas and short-grass areas. Use a $\chi ^ { 2 }$ test at .01 level of significance to decide whether the true proportions of different marks are identical for the two types of regions. $\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\text { Type of mark }$ L LL Y+YL O Others Row Total Long-grass areas 410 12 23 8 277 730 Short-grass areas 515 6 16 13 220 770 Column Total 925 18 39 21 497

A two-way contingency table has r rows and c columns. Then, the number of degrees of freedom associated with the chi-squared test for independence is __________.

The $\chi ^ { 2 }$ goodness-of-fit test statistic, when there are k categories and m parameters to be estimated from the sample data, has approximately a chi-squared distribution with $v$ degrees of freedom, where $v$ equals

Say as much as you can about the P-value for an upper-tailed chi-squared test in each of the following situations: a. $\chi ^ { 2 } = 8.15 , d f = 2$ b. ${ \chi } ^ { 2 } = 13.78 , d f = 6$ c. ${ \chi } ^ { 2 } = 17.46 , d f = 9$ d. $\chi ^ { 2 } = 19.92 , k - 5$ e. ${ \chi } ^ { 2 } = 3.67 , k = 4$

Which of the following statements are not true?

The number of degrees of freedom for a two-way contingency table with I rows and J columns is

In testing $H _ { 0 } : p _ { 1 } = p _ { 10 } , p _ { 2 } = p _ { 20 } , \ldots . . , p _ { 5 } = p _ { 50 }$ versus the alternative $H _ { \pm }$ that states that at least one $p _ { i }$ does not equal $p _ { 10 } ,$ rejection of $H _ { 0 }$ is appropriate at .10 significance level when the test statistic value $\chi ^ { 2 }$ is

One may wish to test $H _ { 0 } : p _ { 1 } = p _ { 10 } , \ldots , p _ {\alpha } = p _ { \alpha 0 } \text { versus } H _ {\pm } : H _ { 0 }$ is not true. The null hypothesis is __________ hypothesis in the sense that each $p _ { 10 }$ is a specified number, so that the expected cell counts when $H _ { 0 }$ is true are uniquely determined numbers.

In a two-way contingency table, if the second row total is 125, the third column total is 60, and the total number of observations is 375, then the estimated expected count in cell (2, 3) is __________.

A study reports the following data on 7-day flexural strength of nonbloated burned clay aggregate concrete samples (psi): 386 456 476 480 490 497 526 546 700 440 393 407 407 434 427 440 407 450 460 327 317 300 340 340 343 374 377 Test at level .10 to decide whether flexural strength is a normally distributed variable.

A study focuses on the existence of any relationship between date of patient admission for treatment of alcoholism and patient's birthday. Assuming a 365-day year more than 90 days from the birthday. A sample of 200 patients gave observed frequencies of 11, 24, 69, and 96 for categories 1, 2, 3, and 4, respectively. State and test the relevant hypotheses using a significance level of .01.

In a two-way contingency table with 3 rows and 5 columns, assume that the second row total is 120 and the fourth column total is 50, and the total number of observations is 600. Then, the estimated expected count in cell (2, 4) is

A two-way contingency table has 3 rows and 5 columns. Then, the number of degrees of freedom associated with the chi-squared test for homogeneity is __________.

The number of degrees of freedom in testing for independence when using a contingency table with 6 rows and 4 columns is: