Exam 9: Large-Sample Tests of Hypotheses

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 the necessary conditions are met, a two-tailed test is being conducted to test the difference between two population proportions. The two sample proportions are and , respectively, and the standard error of the sampling distribution of is 0.04. Then, the calculated value of the test statistic will be 1.50.

Which of the following statements about possible errors in hypothesis tests is correct?

If a hypothesis test leads to incorrectly rejecting the null hypothesis, a Type II error has been committed.

If the probability of committing a Type I error is set at 0.10, then the probability of committing a Type II error will be 0.90, since sum of probabilities must be 1.0.

A manufacturer of copper pipes must produce pipes with a diameter of precisely 5 inches. The firm's quality inspector wants to test the hypothesis that pipes of the proper size are being produced. Accordingly, a simple random sample of 100 pipes is taken from the production process. The sample mean diameter turns out to be 4.98 inches and the sample standard deviation 0.2 inches. Using a significance level of = 0.05, test the appropriate hypotheses. Find the p-value for the test. Test statistic = ______________ p-value = ______________ Conclusion: ______________ Interpretation: __________________________________________

The variance of is V ( ) = .

Suppose that we reject the null hypothesis at the 0 .05 level of significance. Then for which of the following -values do we also reject the null hypothesis?

Increasing the size of the samples in a study to estimate the difference between two population means will increase the probability of committing a Type I error that a decision maker can have regarding the interval estimate.

If H₀ is corroborated in a hypothesis test, no action need be taken by anyone.

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

A statistics professor has claimed that her top student will average more than 98 points in the final exam. If you wish to test this claim, you would formulate the following null and alternative hypotheses: vs. .

When the hypothesized proportion is close to 0.50, the spread in the sampling distribution of the sample proportion is greater than when is close to 0.0 or 1.0.

Which of the following statements is false?

The p-value of a statistical test is the largest value of the significance level for which the null hypothesis can be rejected.

Type II error is typically greater for two-tailed hypothesis tests than for one-tailed tests.

In a one-tailed test, the p-value is found to be equal to 0.036. If the test had been two-tailed, the p-value would have been 0.072.

A two-tail test is a test in which a null hypothesis can be rejected by an extreme result occurring in only one direction.

A sample of size 150 is to be used to test the hypotheses H₀: = 8.3 versus H₁: 8.3 where is the true average weight of a newborn American baby. Give the appropriate rejection region associated with each of the following significance levels. = 0.01 Critical Value(s) = ______________ = 0.05 Critical Value(s) = ______________ = 0.1 Critical Value(s) = ______________

If you wish to estimate the difference between two population means using two independent large samples, the 90% confidence interval estimate can be constructed using which of the following critical values?