Reading 6: Hypothesis Testing

Which of the following statements best describes the null hypothesis?

A researcher wants to test if the mean return on a portfolio is different from zero. The appropriate set of hypotheses is:

A Type I error is defined as:

The power of a hypothesis test is defined as the probability of:

If the significance level of a test is 5 percent and the probability of a Type II error is 20 percent, the power of the test is:

For a two-tailed test using the standard normal distribution at the 5 percent level of significance, the critical z-values are:

A test statistic is calculated as:

The p-value is best described as:

An analyst conducts a hypothesis test and calculates a p-value of 0.03. If the chosen significance level is 0.05, the analyst should:

Which of the following distributions is appropriate for testing a hypothesis about a population mean when the variance is unknown and the sample is large?

A sample of 25 observations has a mean of 10 and a standard deviation of 4. The researcher wants to test if the population mean is greater than 8 at the 5 percent significance level. The standard error of the sample mean is:

Using the data from the previous question (Mean=10, Hypothesized=8, SE=0.8), the calculated test statistic is:

In a one-tailed test with 24 degrees of freedom at the 5 percent significance level, the critical t-value is 1.711. Based on a calculated t-statistic of 2.50, the researcher should:

The distinction between statistical significance and economic significance implies that:

When testing the difference between two population means using two independent samples, the degrees of freedom for the t-test (assuming equal variances) are calculated as:

A paired comparisons test is most appropriate when:

For a paired comparisons test with 20 pairs of observations, the degrees of freedom are:

To test the hypothesis that the variance of a normally distributed population is equal to a specific value, the appropriate test statistic is based on the:

A sample of 15 observations has a standard deviation of 6. The researcher wants to test if the population variance is equal to 25. The calculated chi-square statistic is closest to:

The F-statistic used to test the equality of two variances is calculated as:

Sample A has a variance of 25 (n=21) and Sample B has a variance of 16 (n=16). The calculated F-statistic to test if the variances are equal is:

To test the hypothesis that the population correlation coefficient equals zero, the appropriate test statistic follows a:

A sample of 42 observations shows a correlation coefficient of 0.35. The researcher wants to test if the correlation is different from zero. The degrees of freedom for this test are:

Nonparametric tests are preferred when:

The Spearman rank correlation coefficient is best described as:

A contingency table is used to test:

In a chi-square test for independence with 3 rows and 3 columns, the degrees of freedom are:

Data snooping bias refers to:

Survivorship bias in mutual fund studies typically leads to:

Look-ahead bias occurs when:

If a test statistic is 1.80 and the critical value is 1.65 (one-tailed upper), the decision is to:

Which test statistic is appropriate to test if the mean of a population is equal to zero when the variance is unknown and n=20?

If the null hypothesis is H0: mean <= 0, the alternative hypothesis Ha is:

The critical value for a two-tailed z-test at the 1 percent significance level is closest to:

A confidence interval for a population parameter can be expressed as:

If a 95 percent confidence interval for a mean does not include zero, then:

When the sample size is small and the population is not normally distributed, which test statistic should be used?

For a test of the equality of two variances, the critical F-value depends on:

A researcher assumes that two samples are independent, normally distributed, and have equal variances. The pooled variance is calculated as:

With 20 tests at the 10 percent significance level, the expected number of false positives (Type I errors) if the null hypothesis is true for all is:

Using a higher significance level (e.g., 10 percent instead of 5 percent) will:

A chi-square test for a single variance is:

If a calculated t-statistic is -2.4 and the critical values are +/- 2.1, the decision is:

In a contingency table, the expected frequency for a cell is calculated as:

Which of the following is an example of a nonparametric test?

If sample data has a t-statistic of 2.363 for a correlation test with 40 degrees of freedom (critical value 2.021), we conclude:

Economic significance differs from statistical significance in that:

When testing if the mean of a single population is 50, the null hypothesis should be stated as:

If a researcher decreases the probability of a Type I error (alpha), the probability of a Type II error (beta) will typically:

The test statistic for the Spearman rank correlation follows which distribution when n > 30?