Hypothesis Testing: EOCQ

Identify the appropriate test statistic or statistics for conducting the following hypothesis tests. (Clearly identify the test statistic and, if applicable, the number of degrees of freedom. For example, "We conduct the test using an x-statistic with y degrees of freedom.") B. Ho: μ = 0 versus Ha: μ ≠0 where μ is the mean of a normally distributed population with unknown variance. The test is based on a sample of 40 observations.

we will use a t-statistic because we have an unknown population variance. this will be a two tailed test because we are testing for equality vs inequality. we will have n-1 degrees of freedom so we will have 39 degrees of freedom

When evaluating mean differences between two dependent samples, the most appropriate test is a: A. chi-squared test B. paired comparisons test C. z-test

B. paired comparisons test

Identify the appropriate test statistic or statistics for conducting the following hypothesis tests. (Clearly identify the test statistic and, if applicable, the number of degrees of freedom. For example, "We conduct the test using an x-statistic with y degrees of freedom.") C. Ho: μ ≦ 0 verus Ha: μ > 0 where μ is the mean of a normally distributed population with known variance σ^². The sample size is 45.

This is a right tail test because Ha is μ > 0. (wherever the > /< sign points in the Ha indicates which tail test it is. ) We have a known variance and n > 30 so we will use a z statistic.

Identify the appropriate test statistic or statistics for conducting the following hypothesis tests. (Clearly identify the test statistic and, if applicable, the number of degrees of freedom. For example, "We conduct the test using an x-statistic with y degrees of freedom.") A. Ho: μ = 0 versus Ha: μ≠0 where μis the mean of a normally distributed population with unknown variance. The test is based on a sample of 15 observations

We will use a t statistic because n <30 and we have unknown population variance This is a two tailed test because we are testing for equality vs inequality degrees of freedom at n-1 so here degrees of freedom are 14.

For a small sample with unknown variance, which of the following tests of a hypothesis concerning the population mean is most appropriate a. A t-test if the population is normally distributed b. A t-test if the population is non-normally distributed c. A z-test regardless of the normality of the population distribution

a. A t-test if the population is normally distributed

A chi-square test is most appropriate for tests concerning: a. a single variance b. differences between two population means with variances assumed to be equal c. differences between two population means with variances assumed to not be equal

a. a single variance

In the step "stating a decision rule" in testing a hypothesis, which of the following elements must be specified? a. critical value b. power of a test c. value of a test statistic

a. critical value

A pooled estimator is used when testing a hypothesis concerning the: a. equality of the variances of two normally distributed populations b. difference between the means of two at least approximately normally distributed populations with unknown but assumed equal variances. c. difference between the means of two at least approximately normally distributed populations with unknown but assumed unequal variances.

b. difference between the means of two at least approximately normally distributed populations with unknown but assumed equal variances.

A Type II error is best described as: a. rejecting a true null hypothesis b. failing to reject a false null hypothesis c. failing to reject a false alternative hypothesis

b. failing to reject a false null hypothesis

The probability of correctly rejecting the null hypothesis is the: a. p-value b. power of a test c. level of significance

b. power of a test

A hypothesis test for a normally-distributed population at a 0.05 significance level implies a: a. 95% probability of rejecting a true null hypothesis b. 95% probability of a Type 1 error for a two-tailed test c. 5% critical value rejection region in a tail of the distribution for a one-tailed test

c. 5% critical value rejection region in a tail of the distribution for a one-tailed test

When making a decision in investments involving a statistically significant result, the: a. economic result should be presumed meaningful b. statistical result should take a priority over economic considerations c. economic logic for the future relevance of the result should be further explored

c. economic logic for the future relevance of the result should be further explored.

Which of the following represents a correct statement about the p-value? A. The p-value offers less precise information than does the rejection points approach B. A larger p-value provides stronger evidence in support of the alternative hypothesis C. A p-value less than the specified level of significance leads to rejection of the null hypothesis.

C. A p-value less than the specified level of significance leads to rejection of the null hypothesis.

Identify the appropriate test statistic or statistics for conducting the following hypothesis tests. (Clearly identify the test statistic and, if applicable, the number of degrees of freedom. For example, "We conduct the test using an x-statistic with y degrees of freedom.") D. Ho: σ² = 200 versus Ha: σ² ≠200, where σ²is the variance of a normally distributed population. The sample size is 50.

Since we are testing for equality vs inequality this is a two tailed test. Since we are testing for variance and only looking at 1 variance, we will use a chi² statistic (χ²) Degrees of freedom is n-1. we have 49 degrees of freedom.

Which of the following should be used to test the difference between the variances of two normally distributed populations? a. t-test b. F-test c. paired comparisons test

b. F-test

An analyst is examining the monthly returns for two funds over one year. Both funds' returns are non-normally distributed. To test whether the mean return of one fund is greater than the mean return of the other fund, the analyst can use: a. a parametric test only b. a nonparametric test only c. both parametric and nonparametric tests

b. a nonparametric test only

Which of the following statements is correct with respect to the null hypothesis? a. it is considered to be true unless the sample provides evidence showing it is false. b. it can be stated as "not equal to" provided the alternative hypothesis is stated as "equal to" c. in a two tailed test, it is rejected when evidence supports equality between the hypothesized value and the population parameter.

a. it is considered to be true unless the sample provides evidence showing it is false.

An analyst is examining a large sample with an unknown population variance. To test the hypothesis that the historical average return on an index is less than or equal to 6%, which of the following is the most appropriate test? a. one-tailed z-test b. two-tailed z-test c. one-tailed F-test

a. one-tailed z-test

The value of a test statistic is best described as the basis for deciding whether to: a. reject the null hypothesis b. accept the null hypothesis c. reject the alternative hypothesis

a. reject the null hypothesis

Which of the following is a Type 1 error? a. rejecting a true null hypothesis b. rejecting a false null hypothesis c. failing to reject a false null hypothesis

a. rejecting a true null hypothesis

An analyst tests the profitability of a trading strategy with the null hypothesis being that the average abnormal return before trading costs equals zero. The calculated t-statistic is 2.802, with critical values of +/- 2.756 at significance level 𝛼 = 0.01. After considering trading costs, the strategy's return is near zero. The results are most likely a. statistically but not economically significant b. economically but not statistically significant c. neither statistically nor economically significant

a. statistically but not economically significant they are statistically significant because the t-stat falls outside the rejection range.

Which of the following statements on p-value is correct? a. the p-value is the smallest level of significance at which Ho can be rejected. b. the p-value indicates the probability of making a Type II error c. the lower the p-value, the weaker the evidence for rejecting the Ho.

a. the p-value is the smallest level of significance at which Ho can be rejected.

In which of the following situations would a non-parametric test of a hypothesis most likely be used? a. the sample data are ranked according to magnitude b. the sample data come from a normally distributed population c. the test validity depends on many assumptions about the nature of the population

a. the sample data are ranked according to magnitude

Which of following tests of a hypothesis concerning the population mean is most appropriate? a. A z-test if the population variance is unknown and the sample is small b. A z-test if the population variance is normally distributed with a known variance c. A t-test if the population is non-normally distributed with unknown variance and a small sample

b. A z-test if the population variance is normally distributed with a known variance

Which of the following statements regarding a one-tailed hypothesis test is correct? a. the rejection region increases in size as level of significance becomes smaller b. a one-tailed test more strongly reflects the beliefs of the researcher than a two-tailed test c. the absolute value of the rejection point is larger than that of a two-tailed test at the same level of significance

b. a one-tailed test more strongly reflects the beliefs of the researcher than a two-tailed test

The level of significance of a hypothesis test is best used to: a. calculate the test statistic b. define the test's rejection points c. specify the probability of a Type II error

b. define the test's rejection points

For a small sample from a normally distributed population with unknown variance, the most appropriate test statistic for the mean is the: a. z-statistic b. t-statistic c. χ² statistic

b. t-statistic

The power of a hypothesis test is: a. equivalent to the level of significance b. the probability of not making a Type II error c. unchanged by increasing a small sample size

b. the probability of not making a Type II error probability of making a type II error is β. probability of not making a type II error is (1 - β) also known as the power of a test.

Which of the following statements is correct with respect to the p-value? a. it is a less precise measure of test evidence than rejection points b. it is the largest level of significance at which the null hypothesis is rejected c. it can be compared directly with the level of significance in reaching test conclusions.

c. it can be compared directly with the level of significance in reaching test conclusions.

Which of the following statements about hypothesis testing is correct? a. the null hypothesis is the condition a researcher hopes to support b. the alternative hypothesis is the proposition considered true without conclusive evidence to the contrary c. the alternative hypothesis exhausts all potential parameter values not accounted for by the null hypothesis

c. the alternative hypothesis exhausts all potential parameter values not accounted for by the null hypothesis if Ho : μ = 0 Ha: μ =/ 0