Exam 10: A: Inference From Small Samples

When small samples are used to estimate the true population mean where the population standard deviation is unknown, the margin of error for the confidence interval estimate tends to be very small.

If a sample of size 20 is randomly selected from a population, the value of A for the probability P(-A t A) = 0.95 is 2.093.

Which of the following may be used to describe the sampling distribution of the quantity ?

Two independent samples are selected at random from two normal populations. The sample statistics are as follows: and Assuming that a two-tailed hypothesis test is conducted at α = 0.05, what is the critical value?

The t distribution allows the calculation of confidence intervals for means for small samples when the population variance is not known, regardless of the shape of the distribution in the population.

In testing vs. the critical value is determined from the F distribution table with an upper tail area equal to half the value of the level of significance.

In testing vs. the null hypothesis will be rejected if the ratio is substantially larger than 1.0.

In constructing a 95% confidence interval estimate for the difference between the means of two normally distributed populations, where the unknown population variances are assumed NOT to be equal, summary statistics computed from two independent samples are as follows: , , , , , and . In this case, what is the upper confidence limit?

The test statistic used to test hypotheses about the population variance is , which is chi-square distributed with n - 1 degrees of freedom when the population is normally distributed with variance equal to .

In testing vs. if and then the calculated value of the test statistic is F = 1.60.

In a hypothesis test for a population variance , the chi-square distribution is used to determine the critical value.

Which of the following distributions is used when testing vs.

A random sample of size n has been selected from a normally distributed population. In hypothesis testing for the population mean, when should the t test be used instead of the z test?

The sampling distribution of the ratio of two sample variances / is said to be F distributed provided that the samples are dependent and their sizes are large.

To estimate, with 95% confidence, the average number of kilometres that students living off-campus commute to classes every day, a random sample of 20 students was taken and produced a mean equal to 5.2 km and a standard deviation of 3.05 km. In this case, which of the following is the point estimate for the true population mean?

Which of the following characteristics must hold if the statistic is to be chi-square distributed with n - 1 degrees of freedom?

The F test used for testing the difference in two population variances is always a one-tailed test.

In testing vs. the following sample data were recorded: 5.0, 6.1, and 11.1. In this case, what is the value of the test statistic?

A political analyst in Manitoba surveys a random sample of registered Liberals and compares the results with those obtained from a random sample of registered Conservatives. This would be an example of an experimental design called a paired-difference or matched -pairs design.

Two samples of sizes 25 and 35 are independently drawn from two normal populations, where the unknown population variances are assumed to be equal. Which one of the following values is the number of degrees of freedom of the equal-variances t test statistic?