QUESTION 2 What does the chi-square goodness of fit test for? a) how good the data fits the standard error of the mean b) how good the data fits our hypothesis c) how good the data fits the normal curve d) how good the data fits the standard deviation QUESTION 3 The goodness of fit test can only test one variable? a) True b) False QUESTION 4 Which chi-square test should be used on the following study? An ethologist counted how many times wolves visited four different habitats. a) goodness of fit b) test of independence QUESTION 5 A school psychologist wanted to know if the class size changed from small (n=10), medium (n=25) to large (n=100) and attendance of low and high. a) goodness of fit b) test of independence
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Step 1: The chi-square goodness of fit test is used to analyze how well the data fits a specific distribution or hypothesis. Show more…
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Question 1: Which of the following is NOT one of the problem categories assessed using the chi-square distribution? a) Testing for independence between two events b) Comparing means of two populations c) Assessing goodness of fit for a data set d) Evaluating variability within a population Question 2: What is the relationship between the degrees of freedom (df) and the shape of the chi-square distribution? a) The shape remains constant regardless of df. b) Higher df leads to a more symmetric distribution. c) Lower df leads to a more symmetric distribution. d) The shape depends on the sample size, not df. Question 3: True or False: The chi-square distribution is always positively skewed. a) True b) False Question 4: When conducting a chi-square test of independence, what is the null hypothesis? a) The two events are independent. b) The two events are dependent. c) The means of two populations are equal. d) The data set follows a specific distribution. Question 5: In a chi-square test, if the calculated test statistic is larger than the critical value, what can be concluded? a) The null hypothesis is rejected. b) The null hypothesis is accepted. c) There is not enough information to draw a conclusion. d) The degrees of freedom are incorrect.
Lucas F.
Answer the chi-square questions using the data below. Use α = 0.01? B A 1 2 3 4 1 20 29 11 19 2 9 28 24 21 a) What is the appropriate test statistic? ---Select--- na z-test One-Sample t-test Independent-Samples t-test Related-Samples t-test One-Way ANOVA Within-Subjects ANOVA Two-Way ANOVA Correlation Slope Chi-Square GoF Chi-Square Independence Compute the statistic selected in a): b) Obtain/compute the appropriate values to make a decision about H0. Critical Value = ; Test Statistic = Decision: ---Select--- Reject H0 Fail to reject H0 c) Compute the corresponding effect size(s) and indicate magnitude(s). If not appropriate, input and/or select "na" below. Effect Size = ; Magnitude: ---Select--- na trivial effect small effect medium effect large effect
Adi S.
Expand Your Knowledge: Student's $\mathrm{t}$ Value for Sample $\mathbf{r}$ and for Sample $\mathrm{b}$ It is not obvious from the formulas, but the values of the sample test statistic $t$ for the correlation coefficient and for the slope of the least-squares line are equal for the same data set. This fact is based on the relation $$ b=r \frac{s_{y}}{s_{x}} $$ where $s_{y}$ and $s_{x}$ are the sample standard deviations of the $x$ and $y$ values, respectively. (a) Many computer software packages give the $t$ value and corresponding $P$ -value for $b$. If $\beta$ is significant, is $\rho$ significant? (b) When doing statistical tests "by hand," it is easier to compute the sample test statistic $t$ for the sample correlation coefficient $r$ than it is to compute the sample test statistic $t$ for the slope $b$ of the sample least-squares line. Compare the results of parts (b) and (f) for Problems $7-12$ of this problem set. Is the sample test statistic $t$ for $r$ the same as the corresponding test statistic for $b$ ? If you conclude that $\rho$ is positive, can you conclude that $\beta$ is positive at the same level of significance? If you conclude that $\rho$ is not significant, is $\beta$ also not significant at the same level of significance?
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