Question 36 of 50

You compute a Pearson sample correlation r = 0.35 from n = 12 paired observations. Using the parametric t-test for correlation, calculate the t-statistic and determine whether r is significantly different from zero at the two-sided 5 percent level (critical t approximately ±2.201).

You have paired data on two variables for n = 35 observations and compute the Spearman rank correlation coefficient rs = 0.6916. Using the large-sample t-approximation (t = rs * sqrt((n-2)/(1-rs^2))), compute the t-statistic and decide whether rs is significantly different from zero at the two-sided 5 percent level (critical t ≈ ±2.0345).

You have a 3x3 contingency table (three rows, three columns) of counts. Which formula gives the expected frequency Eij for cell (i,j) under the null hypothesis of independence, and what are the degrees of freedom for the chi-square test of independence?

A 3x3 contingency table of 1,594 ETFs by Size (small, medium, large) and Investment Type (value, growth, blend) yields a chi-square statistic = 32.08 and df = 4. Using a 5 percent significance level (chi-square critical ≈ 9.4877), what conclusion should you draw?

You calculate Pearson correlation r = 0.8277 between Fund 1 monthly returns and the S&P 500 using n = 36 months. Using the parametric t-test for correlation, is r different from zero at the two-sided 5 percent level? (critical t ≈ ±2.032).

In computing the Spearman rank correlation coefficient rs for n = 9 observations you find tied ranks for two observations in one variable (a tie for the 3rd and 4th largest values). How should you assign ranks for the tied observations before computing di and di^2?

You compute a Spearman rank correlation rs = -0.20417 for n = 9 funds comparing alpha and expense ratio. The t-statistic (using t = rs * sqrt((n-2)/(1 - rs^2))) equals about -0.552. With critical t-values ±2.306 at the 0.05 level, what decision is appropriate?

In a contingency table test of independence, the standardized residual for a cell is (Oij - Eij)/sqrt(Eij). If for a particular cell you get Oij = 122, Eij = 87.48, what is the standardized residual and what does a value above +2 imply?

Which situation is LEAST appropriate for applying a parametric Pearson correlation test?

You have two independent samples and wish to test for association between group membership and categorical outcome (2 categories by 3 categories contingency). What test should you use and what is the df formula?

In the ETF contingency example, medium-growth cell observed count O = 122 and expected E = 87.48 produced a scaled squared deviation contribution ((O-E)^2)/E of about 13.62. How much does this cell contribute to the total chi-square value of 32.080? (Percentage contribution)

Which of the following correctly states when to prefer nonparametric tests over parametric tests?

You have the following 2x3 contingency table: Row totals = [120, 130] columns totals = [100, 90, 60]. Overall total = 250. What is the expected frequency for cell (row1, col2)?

An analyst computes the Pearson sample correlation r between two variables as 0.31 with n = 36. The t-statistic calculated for correlation is 1.903. Given critical t ≈ ±2.032 at the two-sided 5 percent level, what is the p-value approximate range and decision?

Which test statistic is used in a chi-square test of independence and what main inputs are required?

An analyst computes Pearson correlation r = 0.3102 between two funds with n = 36 and finds t = 1.903 and p approximately 0.06 (two-sided). What interpretation is correct at the 5 percent level?

When constructing a chi-square test of independence, which of the following is a required assumption for the usual chi-square approximation to be valid?

You test independence in a 3x3 table and find chi-square = 5.5 with df = 4. For alpha = 0.05, the critical chi-square is 9.4877. Which conclusion is correct?

Which statement about Spearman rank correlation is TRUE?

In a 3x3 contingency table, you find several cells have small expected values (<5). Which action is MOST appropriate before performing a chi-square test?

You have a contingency table and compute chi-square = 12.8 with df = 4. What is the approximate p-value range (using chi-square criticals: at 0.01 -> 13.277, at 0.025 -> 11.143)?

Which of the following is TRUE about degrees of freedom for the chi-square test of independence in an r by c table?

Suppose you compute a chi-square statistic of 3.57 for a 2x2 contingency table (df = 1). What is the two-sided p-value approximate and decision at alpha = 0.05? (chi-square critical at 0.05 with df=1 is 3.841)

A dataset for two categorical variables yields expected cell counts all above 10 and total sample large. Which test is appropriate and why might nonparametric vs parametric labels be confusing here?

You perform a chi-square test of independence on a 3x2 table and get chi-square = 46.3223 with df = 4. If the critical value at alpha = 0.05 is 9.4877, what do you conclude and what might be next steps to understand the association?

A 3x3 contingency table yields chi-square = 32.08 with df = 4 and p < 0.001. Which statement about Type I and Type II errors aligns with this outcome?

Which of these statements about the chi-square test of independence is FALSE?

In the ETF example, a mosaic plot shows a large dark cell for medium-growth ETFs. The standardized residual for that cell is +3.69. How should you interpret this?

When computing Spearman rs across many pairs (e.g., 10 unique currency pairs) and testing each at the 5 percent level, which multiplicity issue should you consider and why?

Which of the following best describes the relationship between sample size and the ability to detect a nonzero Pearson correlation?

A researcher tests independence in an r x c table using chi-square and obtains chi-square = 18.63 with df = 6. Using the chi-square critical values table, what is the approximate p-value range (chi-square critical for df=6: at 0.05 -> 12.592, at 0.01 -> 16.812)?

Which of the following descriptions correctly distinguishes the Pearson parametric correlation test from the Spearman nonparametric test?

A researcher has a contingency table of 500 companies classified by environmental rating (3 levels) and governance rating (3 levels). She computes chi-square = 35.744 and df = 4. With chi-square critical at 0.05 equal to 9.4877, interpret the result.

If you wish to test whether a contingency table classification shows an association in a one-sided direction (e.g., more of category A in row1 than expected), how can you use standardized residuals in addition to the overall chi-square?

You compute Pearson r between two series over many sample sizes. Which trend regarding the required magnitude of r to achieve significance is correct?

An analyst wants to compare two period return distributions (Period 1 and Period 2) using daily returns where samples are independent and not paired. Which approach is appropriate to test whether mean returns differ?

You have computed Spearman rs matrix for five exchange rates over 180 days and found all pairwise correlations significant at 5 percent. Which of the following is reasonable next-step interpretation?

Which of these calculations do you need to compute the chi-square statistic for a contingency table cell (i,j)?

An analyst runs Spearman correlations among many pairs and obtains several small p-values around 0.04. What is the best general advice regarding interpretation?

When using Spearman rank correlation on five currencies over 180 days (10 unique pairs), the analyst finds all pairwise t-statistics well above critical value; which interpretation about independence is correct at 5 percent?

Which of the following correctly states the null hypothesis commonly tested for Pearson correlation in financial time series context?

A 3x3 contingency table test returns chi-square = 1.902 with df = 4. For alpha = 0.05, what is the decision?

If you compute Spearman rs on small samples (n <= 30), what special consideration should you take when testing significance?

Which of the following is a correct reason to prefer a Spearman test over a Pearson test for correlation?

In a 3x3 contingency table of ETFs you compute expected frequency for small-value cell as 46.703 and observed O = 50. The cell's scaled squared deviation equals (O - E)^2 / E. Compute that value roughly.

If you find a statistically significant chi-square for independence in a large contingency table, which practical step helps prioritize which deviations are most important?

Which is the correct degrees of freedom for a chi-square test on a 4x5 contingency table?

You have observed that pairing categorical labels into fewer categories before a chi-square test increases expected counts and may help the test validity. Which caution should you heed when doing this?

Which measure complements chi-square results by quantifying effect size for association in contingency tables, particularly when sample sizes are large?