Exam 9: A: large-Sample Tests of Hypotheses

In estimating the difference between two population means, the estimate for the standard deviation of the sampling distribution of is found by taking the square root of the sum of the two sample variances.

If you wish to construct a confidence interval estimate for the difference between two population means, what would an increase in the sample sizes used result in?

When testing vs. , the observed value of the z-score was found to be -2.15. What is the p-value for this test?

What is the rejection region for testing at the 0.05 level of significance?

A two-tailed test of hypothesis for a population mean with a significance level equal to 0.05 will have a critical value z equal to 0.475.

Which of the following would be an appropriate null hypothesis to test a proportion?

If the power of a statistical test is 0.9207, then the probability of accepting a false null hypothesis is 0.0793.

A one-tailed hypothesis test of the population proportion is used when the alternative hypothesis takes the form

Which of the following conditions must hold before one can make use of the standard normal distribution for constructing a confidence interval estimate for the population proportion p?

The z-test can be used to determine whether two population means are equal.

The necessary conditions having been met, a two-tailed test is being conducted to test the difference between two population proportions. The two sample proportions are and , and the standard error of the sampling distribution of is 0.0085. Under these circumstances, the calculated value of the test statistic will be z = 3.41.

The sampling distribution of is normal if the sampled populations are normal, and approximately normal if the populations are non-normal and the sample sizes and are large.

The probabilities of committing Type I and Type II errors are related such that when one is increased, the other will increase as well.

If you wish to test whether two populations means are the same, the appropriate null and alternative hypotheses would be vs.

The p-value or observed significance level measures the strength of the evidence against the alternative hypothesis.

The sampling distribution of is approximately normal, provided that the sample size is large enough (n > 30).

Suppose in testing a hypothesis about a proportion, the z test statistic is computed to be 1.92. The null hypothesis should be rejected if the chosen level of significance is 0.01 and a two-tailed test is used.

When formulating a hypothesis test about a population mean, the alternative hypothesis should avoid using an equality.

The necessary conditions having been met, a lower-tailed test is being conducted for the difference between two population proportions. If the value of the test statistic is -2.43, then the null hypothesis cannot be rejected at = 0.025.

Suppose in testing a hypothesis about a proportion, the p-value is computed to be 0.038. The null hypothesis should be rejected if the chosen level of significance is 0.05.