Learning Module 8 Hypothesis Testing

An analyst tests H0: mu = 0.05 versus Ha: mu > 0.05 using a one-sample t-test with n = 25 and obtains t = 1.75. Using a 5 percent significance level, the critical t-value (one-sided) is approximately 1.711. What should the analyst conclude?

A fund manager wishes to test whether annual returns differ between two independent samples: sample A (n1 = 40, mean = 8.0, sd = 10.0) and sample B (n2 = 50, mean = 5.0, sd = 8.0). Assuming equal population variances, what is the pooled estimate of variance (sp^2)?

You want to test whether the variance of monthly returns for a fund is less than 0.04 (i.e., sigma^2 < 0.04). You have n = 20, sample variance s^2 = 0.06. Which test statistic and decision rule are appropriate (left-tailed test) at alpha = 0.05?

A researcher computes correlation r = 0.35 from n = 32 paired observations. Which test and degrees of freedom should be used to test H0: rho = 0?

Two yearly periods produce independent samples of daily returns. Period 1: n1 = 445, mean1 = 0.01775 percent, var1 = 0.09973^2 (use s1^2 = 0.09973). Period 2: n2 = 859, mean2 = 0.01134 percent, var2 = 0.15023^2 (use s2^2 = 0.15023). Assuming equal variances, what is the pooled variance sp^2 used for the two-sample t-test?

An analyst runs a chi-square test for independence on a 3x3 contingency table with r = 3 rows and c = 3 columns. What are the degrees of freedom for the chi-square test?

You observe a sample correlation r = 0.3102 from n = 36 observations. Using a two-sided 5 percent test (critical t ≈ ±2.032 for df = 34), the calculated t-statistic is 1.903. What is the conclusion?

Which statement correctly describes the relation between significance level alpha and Type II error beta, all else equal?

An analyst has two dependent samples (paired): before and after returns for the same assets. Which test is most appropriate to test for a mean difference?

You run a two-sided test of H0: mu = mu0 using t-statistic and get p-value = 0.032. Which of the following is correct at alpha = 0.05?

A two-sample F-test compares variances s1^2 and s2^2 from independent normal samples with sizes n1 and n2. If the calculated F = s1^2 / s2^2 = 1.185 and critical values for two-tailed 5 percent are 0.82512 and 1.21194, what is the conclusion?

Which nonparametric test is the appropriate rank-based alternative to the two-sample independent t-test (comparing medians) when assumptions of normality are violated?

A manager tests H0: mu <= 5% versus Ha: mu > 5% and selects alpha = 0.05. Which tail(s) contain the rejection region and what is the nature of the test?

Which of the following best describes a Type I error in hypothesis testing?

In a test of difference between two independent means with unknown and unequal variances, which approach is appropriate?

An analyst tests whether the standard deviation of returns is less than 4 percent using n = 24, s = 3.6 percent, sigma0 = 4 percent, alpha = 0.05 (one-sided left test). The chi-square test statistic is (n - 1)s^2 / sigma0^2 = 23*0.1296 / 0.16 = 18.63. The critical chi-square left-tail value is approximately 13.09. How to conclude?

Which of the following is TRUE about p-values?

A contingency table chi-square test yields total chi-square = 32.08 with df = 4 and critical chi-square (0.95, 4) = 9.488. What conclusion about independence of classifications should be drawn at 5 percent?

Which test statistic (distribution) is appropriate for testing H0: mu = mu0 when population is approximately normal and sigma is unknown?

An analyst uses a dummy (indicator) variable equal to 1 in months with earnings announcements and 0 otherwise, regressing monthly returns on this indicator. The estimated slope on the indicator equals 1.21 with t = 10.44. What does the slope measure?

Which of the following best describes the power of a test?

In testing H0: sigma1^2 = sigma2^2 for two independent normal populations using sample variances s1^2 and s2^2, an F-statistic is formed as F = s1^2 / s2^2. If n1 = 50, n2 = 50, s1^2 = 4.644, s2^2 = 3.919, what is F and how to interpret at 5 percent two-tailed (critical upper ≈ 1.21194 and lower ≈ 0.82512)?

When should an analyst prefer nonparametric tests over parametric tests?

Which test and degrees of freedom apply to test whether regression slope b1 equals zero in a simple linear regression estimated with n observations?

If you wish to test whether two categorical variables are independent, which test do you use and what input is required?

A researcher pools two years of quarterly returns even though strategies changed between years, obtaining a lower Sharpe ratio for the pooled data than for each year separately. What is the likely reason?

An analyst computes Spearman rank correlation r_s = 0.6916 using n = 35. For a two-sided test at alpha = 0.05, what test statistic and df are used to test H0: r_s = 0?

In a test concerning a single variance using chi-square with df = n - 1, why must the population be normally distributed for the chi-square test to be valid?

A statistician wants to compare means of two independent samples where observations are strongly non-normal and contain outliers. Which approach is most appropriate?

If you observe a calculated F-statistic in regression of 16.01 with df1 = 1 and df2 = 4, and the 5 percent critical F is 7.71, what conclusion can be drawn about the null that the slope equals zero?

Which of the following is a correct interpretation of a 95 percent confidence interval for a mean constructed from sample data?

An analyst has sample correlation r = -0.1452 with n = 248. The t-statistic using formula t = r sqrt((n-2)/(1-r^2)) is -2.302. Using two-sided 5 percent critical approximately ±1.967, what can the analyst conclude?

Which statement best summarizes the distinction between standard deviation and standard error?

Which of the following is an appropriate two-sided null and alternative hypothesis concerning a population correlation coefficient rho?

What is the effect of increasing sample size on the sampling distribution of the sample mean according to the central limit theorem?

Which test statistic and distribution are appropriate when testing equality of two population means using two independent samples with unknown but equal variances?

You fit a linear regression and obtain t-statistic for slope = 4.00 with df = 4. What is the two-sided p-value roughly (note t=4.00 corresponds to small p)?

When estimating a regression slope, which of the following will reduce the standard error of the slope estimate, all else equal?

Which of these is the correct formula for the expected frequency Eij in a contingency table under independence?

A fund returned mean monthly 1.5% with sample sd = 3.6% and n = 24. Test whether mean differs from 1.1% at 5 percent two-sided. Compute t = (1.5 - 1.1) / (3.6 / sqrt(24)) = 0.544. Given critical t ±2.069 (df 23), conclusion?

Which of these is TRUE about one-tailed versus two-tailed tests at same alpha level?

Which test is appropriate to compare two variances from independent normal samples?

An analyst obtains p-value = 0.056 in a two-sided test at alpha = 0.05. Which is correct?

Which is the correct test for assessing whether the sample median differs from hypothesized value when no analytical standard error formula available?

Which statistic should be used to test H0: sigma^2_before = sigma^2_after for two equal-sized samples each with n = 120 and observed variances s_before^2 = 22.367 and s_after^2 = 15.795 at alpha = 0.05?

If residuals from a regression show a clear U-shaped pattern when plotted against X, which regression assumption is most likely violated?

Why might an analyst prefer a nonparametric test like Wilcoxon signed-rank over a t-test when analyzing paired data?

When performing a test of equality of two means based on independent samples with unknown but equal variances, the t-statistic denominator uses pooled variance. How is pooled variance estimated?

A regression of Y on X yields residual standard error se = 3.46 and sum((Xi - Xbar)^2) = 122.64. What is the standard error of slope b_hat1?

Which of the following best summarizes when to use Spearman rank correlation instead of Pearson correlation?