Question 1

When cell frequencies are small and 2x2 tables are used in the chi square test,an adjustment to the value of chi square can be made by applying
A)Yate's correction for continuity
B)a different value to the expected frequencies
C)a different value to the observed frequencies
D)any of these

Accepted Answer

When cell frequencies are small, using 2x2 tables in the chi-square test leads to inaccurate results. Therefore, Yates' correction for continuity should be applied to adjust the value of chi-square. It reduces the degree of freedom by 1 and makes the test more accurate. The correction is used to account for the difference between the discrete distribution of the observed data and the continuous distribution assumed in the chi-square test. Therefore, Yates' correction is the best choice to adjust the value of chi-square when cell frequencies are small and 2x2 tables are used.

Question 2

If Chi square obtained has a negative value
A)an arithmetic error has been made.
B)a one-tailed test is called for.
C)the row and column variables must be switched.
D)the null hypothesis must be rejecteD.

Accepted Answer

The Chi square test statistic should always be positive. If a negative value is obtained, it indicates an arithmetic error in the calculations.

Question 3

For the chi square test using very large samples,there may be a difference between
A)randomness and independence.
B)expected and calculated frequencies.
C)statistical significance and importance.
D)dependent variables and dependent relationships.

Accepted Answer

The answer of For the chi square test using very...

Question 4

The sampling distribution for chi squares is
A)shaped like any other normal curve.
B)not normally distributed.
C)bimodal.
D)all of these

Accepted Answer

The sampling distribution for chi squares is not normally distributed. It is positively skewed and can be asymmetrical depending on the sample size and degrees of freedom.

Question 5

A problem with large samples in the chi square test is that the test statistic
A)increases at the same rate as sample size and trivial relationships may seem important.
B)decreases as sample size increases and may cause Type I errors.
C)fluctuates so much that the results are completely unreliable.
D)is always elevated above the neutral area.

Accepted Answer

With large samples, even trivial relationships may become statistically significant due to the increase in sample size. This is because the chi square test statistic increases at the same rate as sample size, making it more likely to detect small differences that may not be meaningful in practical terms.

Question 6

In the Chi square test,degrees of freedom are A)N - 1. B)N₁ + N₂ - 2. C)(r + 1)(c + 1). D)(r - 1)(c - 1).

Accepted Answer

The degrees of freedom in the chi-square test are calculated as (r - 1)(c - 1), where r is the number of rows and c is the number of columns in the contingency table. This formula accounts for the fact that the total number of observations in the table is fixed and the expected frequencies can be determined based on the row and column totals. Therefore, the correct choice is (r - 1)(c - 1), which is option D.

Question 7

In the Chi square test for independence,the research hypothesis is
A)always one-tailed.
B)the variables are dependent.
C)the variables are independent.
D)expected frequencies are greater than observed frequencies.

Accepted Answer

The research hypothesis in the chi square test for independence is that the variables are dependent. This means that there is a significant relationship between the two variables being studied. The null hypothesis, on the other hand, is that the variables are independent. Therefore, the best choice is B, as this statement accurately reflects the research hypothesis in this statistical test. A is incorrect because the research hypothesis is not always one-tailed. C is incorrect because it describes the null hypothesis, not the research hypothesis. D is incorrect because the expected frequencies should equal the observed frequencies if the null hypothesis is true.

Question 8

Chi square has been used to test the relationship between gender and support for abortion.The null hypothesis has been rejected.What may be concluded?
A)support for abortion depends on gender
B)gender and support for abortion are not related
C)females are more supportive of abortion
D)males are more supportive of abortion

Accepted Answer

The rejection of the null hypothesis indicates that gender and support for abortion are related. Thus, support for abortion depends on gender. Option A is the best choice.

Question 9

A researcher reports that her obtained chi square of -17.56 is significant because it exceeds the critical Chi square of -3.841 for an alpha of .05 with 2 degrees of freedom.What mistake has been made?
A)neither critical nor obtained Chi squares can have negative values
B)it is impossible to have only 2 degrees of freedom
C)it is impossible for obtained Chi square to exceed 10
D)a one-tailed test should have been used

Accepted Answer

Neither critical nor obtained Chi squares can have negative values. This suggests that the researcher has made an error in report or calculation.

Question 10

A Chi square test has been conducted to assess the relationship between marital status and church attendance.The obtained Chi square is 23.45 and the critical Chi square is 9.488.What may be concluded?
A)reject the null hypothesis,church attendance and marital status are dependent
B)reject the null hypothesis,church attendance and marital status are independent
C)fail to reject the null hypothesis,church attendance and marital status are dependent
D)fail to reject the null hypothesis,church attendance and marital status are independent

Accepted Answer

The obtained Chi square (23.45) is greater than the critical Chi square (9.488), which means that the null hypothesis (Church attendance and marital status are independent) is rejected. Therefore, we can conclude that church attendance and marital status are dependent.

Question 11

For Chi square,a small sample is one in which
A)many expected frequencies are less than 5.
B)many observed frequencies are less than 5.
C)N is less than 100.
D)N is less than 50.

Accepted Answer

For Chi square test, a small sample is defined as one in which many expected frequencies are less than 5. This is because when the expected frequencies are less than 5, the assumptions of the Chi square test are likely to be violated, leading to unreliable results. Therefore, in such cases, it is recommended to use alternative tests such as Fisher's exact test.

Question 12

Yate's correction for small sample size A)reduces the value of the difference between f_o and f_e by .5 before squaring. B)increases the value of the difference between f_o and f_e by .5 before squaring. C)reduces the degrees of freedom by one half. D)increases the degrees of freedom by one half.

Accepted Answer

Yates' correction for continuity is a statistical method to improve the accuracy of the chi-squared test when expected frequencies are small. It involves reducing the absolute difference between the observed and expected frequencies in each cell by 0.5 before taking the square and summing the terms. This helps to adjust for the discreteness of the distribution and provides a better approximation of the p-value for the test. Therefore, option A is correct as it states that the correction reduces the value of the difference between observed and expected frequencies by 0.5 before squaring.

Question 13

How many degrees of freedom does a 3x3 bivariate table have?
A)8
B)6
C)4
D)3

Accepted Answer

For a 3x3 bivariate table, the degrees of freedom can be calculated using the formula (number_of_rows - 1) x (number_of_columns - 1). Therefore, the degrees of freedom for a 3x3 table would be (3-1) x (3-1) = 4. Therefore, the best choice is C.

Question 14

The value of the chi square test statistic is always
A)zero or a positive number.
B)greater than the number of cells in the bivariate table.
C)equal to or greater than the critical value.
D)greater than the degrees of freedom.

Accepted Answer

The chi square test statistic cannot be negative since it is based on squared differences. It can be zero if there is a perfect association between the variables, but otherwise it will always be a positive number.

Question 15

In the Chi square test for independence,the null hypothesis and the research hypothesis
A)always contradict each other.
B)always agree with each other.
C)are never actually stated.
D)are usually both rejecteD.

Accepted Answer

The null hypothesis and the research hypothesis in the Chi square test for independence always contradict each other. The null hypothesis states that there is no significant relationship between two categorical variables, while the research hypothesis suggests that there is a significant relationship between them. Therefore, if one hypothesis is rejected, the other is accepted.

Question 16

In a research study conducted to determine if arrests were related to the socioeconomic class of the offender,the chi square critical score was 9.488 and the chi square test statistic was 12.2.We can conclude that
A)the variables are independent.
B)being in a certain socioeconomic class causes arrests.
C)the variables are dependent.
D)the probability of getting these results by random chance alone is 0.5.

Accepted Answer

The chi square test statistic (12.2) exceeds the critical score (9.488), indicating that there is a significant relationship between the variables (socioeconomic class and arrests), and therefore they are dependent. Option A is incorrect because if the variables were independent, the chi square test statistic would be lower than the critical score. Option B is incorrect because the study only found a correlation between the variables, and not a causation. Option D is incorrect because the probability value cannot be determined from the given information.

Question 17

An obtained chi square of 10.78 has been calculated.Critical Chi square is 3.841.What should be concluded?
A)nothing¾information is incomplete
B)reject the null hypothesis,the variables are not independent
C)reject the null hypothesis,the variables are independent
D)fail to reject the null hypothesis

Accepted Answer

The obtained chi-square value of 10.78 is greater than the critical chi-square value of 3.841. This indicates that the probability of obtaining such a large difference between the observed and expected values is very low. Therefore, we reject the null hypothesis and conclude that the variables are not independent.

Question 18

In a 2x2 table,if one cell frequency is known,
A)all other cell frequencies are determined
B)two other cell frequencies are determined
C)one other cell frequency is determined
D)none of the other cell frequencies is determined

Accepted Answer

The answer of In a 2x2 table,if one cell frequency...

Question 19

Some potential difficulties arise in the chi square test when
A)sample size is small.
B)sample size is very large.
C)many cells have expected frequencies of five or less.
D)all of these

Accepted Answer

All of these options can create potential difficulties in the chi square test. 
When sample size is very small, the chi square distribution may not be a good approximation, leading to inaccurate results. 
When sample size is very large, small deviations from expected frequencies may lead to statistically significant results even if the deviations are not practically significant. 
When many cells have expected frequencies of five or less, this violates the assumption of the chi square test and may lead to inaccurate results. Therefore, none of these scenarios are ideal for conducting a reliable chi square test.

Question 20

A researcher reports a c² (obtained)of 75.34 (a =.05,df = 1,c² (critical)= 3.84,N = 13,678).The researcher claims that the relationship is extremely significant.What issue should be raised? A)degrees of freedom are much too small for a sample this large. B)alpha is too low C)sample size is very large and the actual relationship between the variables might be trivial D)the value for c² (critical)is much too low

Accepted Answer

With such a large sample size, even a small correlation coefficient could be deemed statistically significant. Therefore, the actual relationship between the variables may not be practically significant, despite the statistically significant result.

Quiz 11: Hypothesis Testing Iv: Chi Square

When cell frequencies are small and 2x2 tables are used in the chi square test,an adjustment to the value of chi square can be made by applying

If Chi square obtained has a negative value

For the chi square test using very large samples,there may be a difference between

The sampling distribution for chi squares is

A problem with large samples in the chi square test is that the test statistic

In the Chi square test,degrees of freedom are

In the Chi square test for independence,the research hypothesis is

Chi square has been used to test the relationship between gender and support for abortion.The null hypothesis has been rejected.What may be concluded?

A researcher reports that her obtained chi square of -17.56 is significant because it exceeds the critical Chi square of -3.841 for an alpha of .05 with 2 degrees of freedom.What mistake has been made?

A Chi square test has been conducted to assess the relationship between marital status and church attendance.The obtained Chi square is 23.45 and the critical Chi square is 9.488.What may be concluded?

For Chi square,a small sample is one in which

Yate's correction for small sample size

How many degrees of freedom does a 3x3 bivariate table have?

The value of the chi square test statistic is always

In the Chi square test for independence,the null hypothesis and the research hypothesis

In a research study conducted to determine if arrests were related to the socioeconomic class of the offender,the chi square critical score was 9.488 and the chi square test statistic was 12.2.We can conclude that

An obtained chi square of 10.78 has been calculated.Critical Chi square is 3.841.What should be concluded?

In a 2x2 table,if one cell frequency is known,

Some potential difficulties arise in the chi square test when

A researcher reports a c² (obtained) of 75.34 (a =.05,df = 1,c² (critical) = 3.84,N = 13,678) .The researcher claims that the relationship is extremely significant.What issue should be raised?