Exam 10: A: Inference From Small Samples

In testing the difference between two population means using two independent samples, the sampling distribution of the sample mean difference is normal if the sample sizes are both greater than 30.

Even though the t distribution is mound-shaped, as the degrees of freedom get smaller, the t distribution's dispersion also decreases.

In a hypothesis test for the population variance, the hypotheses are vs. . The sample size is 15 and the test is being carried out at the 10% level of significance. What would be the rejection region?

The chi-square distribution is skewed to the left (negatively skewed), but as degrees of freedom increase, it approaches the shape of the binomial distribution.

In a hypothesis test for the population variance, the hypotheses to be tested are vs. . The sample size is 20 and the test is being carried out at the 10% level of significance. Under which of the following conditions would the null hypothesis be rejected? A) B) C) D)

A researcher wants to test for the equality of two population variances when the populations are normally distributed. He has opted for a10% level of significance . Which of the following upper-tail areas of the F table must he use to determine the rejection region?

In a hypothesis test for a population variance , the null hypothesis is stated in terms of .

In forming a 95% confidence interval for a population mean from a sample size of 20, the number of degrees of freedom from the t distribution equals 18.

Suppose that a one-tailed t-test is being applied to find out if the population mean is less than 100. The level of significance is 0.05 and 25 observations were sampled. Which of the following best describes the rejection region?

We are testing for the difference between the means of two dependent populations (matched pairs experiment) with samples sizes of and . What would be the number of degrees of freedom?

In constructing a confidence interval estimate for the difference between the means of two normally distributed populations, using two independent samples, which of the following approaches should we follow?

Statisticians have shown that for given sample sizes and , the number of degrees of freedom associated with the equal-variances test statistic and confidence interval estimator of is always greater than or equal to number of degrees of freedom associated with the unequal-variances test statistic and confidence interval estimator.