Quantitative Methods 【Reading 11】Sample statements, testing, following, hypothesis

Mechanic

Which of the following statements about testing a hypothesis using a Z-test is least accurate?

A) If the calculated Z-statistic lies outside the critical Z-statistic range, the null hypothesis can be rejected.

B) The calculated Z-statistic determines the appropriate significance level to use.

C) The confidence interval for a two-tailed test of a population mean at the 5% level of significance is that the sample mean falls between ±1.96 σ/√n of the null hypothesis value.

---

The significance level is chosen before the test so the calculated Z-statistic can be compared to an appropriate critical value.

terpsichorefan

The hypothesis testing is the trickiest part to me..... thanks a lot!

torontoanalyst

Which of the following statements about parametric and nonparametric tests is least accurate?

A) Parametric tests are most appropriate when a population is heavily skewed.

B) Nonparametric tests have fewer assumptions than parametric tests.

C) Nonparametric tests are often used in conjunction with parametric tests.

---

For a distribution that is non-normally distributed, a nonparametric test may be most appropriate. A nonparametric test tends to make minimal assumptions about the population, while parametric tests rely on assumptions regarding the distribution of the population. Both kinds of tests are often used in conjunction with one another.

torontoanalyst

Which of the following statements about parametric and nonparametric tests is least accurate?

A) The test of the difference in means is used when you are comparing means from two independent samples.

B) Nonparametric tests rely on population parameters.

C) The test of the mean of the differences is used when performing a paired comparison.

---

Nonparametric tests are not concerned with parameters; they make minimal assumptions about the population from which a sample comes. It is important to distinguish between the test of the difference in the means and the test of the mean of the differences. Also, it is important to understand that parametric tests rely on distributional assumptions, whereas nonparametric tests are not as strict regarding distributional properties.

torontoanalyst

In order to test if Stock A is more volatile than Stock B, prices of both stocks are observed to construct the sample variance of the two stocks. The appropriate test statistics to carry out the test is the:

A) Chi-square test.

B) t test.

C) F test.

---

The F test is used to test the differences of variance between two samples.

torontoanalyst

Abby Ness is an analyst for a firm that specializes in evaluating firms involved in mineral extraction. Ness believes that the earnings of copper extracting firms are more volatile than those of bauxite extraction firms. In order to test this, Ness examines the volatility of returns for 31 copper firms and 25 bauxite firms. The standard deviation of earnings for copper firms was $2.69, while the standard deviation of earnings for bauxite firms was $2.92. Ness’s Null Hypothesis is σ12 = σ22. Based on the samples, can we reject the null hypothesis at a 95% confidence level using an F-statistic and why? Null is:

A) rejected. The F-value exceeds the critical value by 0.849.

B) not rejected. The critical value exceeds the F-value by 0.71.

C) rejected. The F-value exceeds the critical value by 0.71.

---

F = s12 / s22 = $2.922 / $2.692 = 1.18
From an F table, the critical value with numerator df = 24 and denominator df = 30 is 1.89.

torontoanalyst

The test of the equality of the variances of two normally distributed populations requires the use of a test statistic that is:

A) z-distributed.

B) Chi-squared distributed.

C) F-distributed.

---

The F-distributed test statistic, F = s12 / s22, is used to compare the variances of two populations.

torontoanalyst

A test of the population variance is equal to a hypothesized value requires the use of a test statistic that is:

A) F-distributed.

B) t-distributed.

C) Chi-squared distributed.

---

In tests of whether the variance of a population equals a particular value, the chi-squared test statistic is appropriate.

torontoanalyst

Which of the following statements about the variance of a normally distributed population is least accurate?

A) The Chi-squared distribution is a symmetric distribution.

B) The test of whether the population variance equals σ02 requires the use of a Chi-squared distributed test statistic, [(n − 1)s2] / σ02.

C) A test of whether the variance of a normally distributed population is equal to some value σ02, the hypotheses are: H0: σ2 = σ02, versus Ha: σ2 ≠ σ02.

---

The Chi-squared distribution is not symmetrical, which means that the critical values will not be numerically equidistant from the center of the distribution, though the probability on either side of the critical values will be equal (that is, if there is a 5% level of significance and a two-sided test, 2.5% will lie outside each of the two critical values).

torontoanalyst

The variance of 100 daily stock returns for Stock A is 0.0078.  The variance of 90 daily stock returns for Stock B is 0.0083.  Using a 5% level of significance, the critical value for this test is 1.61. The most appropriate conclusion regarding whether the variance of Stock A is different from the variance of Stock B is that the:

A) variances are equal.

B) variance of Stock B is significantly greater than the variance of Stock A.

C) variances are not equal.

---

A test of the equality of variances requires an F-statistic. The calculated F-statistic is 0.0083/0.0078 = 1.064. Since the calculated F value of 1.064 is less than the critical F value of 1.61, we cannot reject the null hypothesis that the variances of the 2 stocks are equal.