Exam 9: A: large-Sample Tests of Hypotheses

In testing vs. a random sample of size 200 produced a sample proportion Given these results, what is the approximate p-value of the test?

In a one-tailed test, the larger the significance level , the larger the critical value will be.

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

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 -2.50, then the p-value is 0.0062.

A professor of statistics refutes the claim that the proportion of Conservative voters in Alberta is at most 44%. To test the claim, the hypotheses , , should be used.

The necessary conditions having been met, an upper-tailed test is being conducted for the difference between two population proportions. If the value of the test statistic is 2.90, then the p-value is 0.0038.

A p-value is a statistic computed from a simple random sample taken from the population of interest in a hypothesis test and then used for establishing the probable truth or falsity of the null hypothesis.

When formulating a hypothesis test, the null hypothesis should be written in such a way so as to minimize the probability of committing a Type I error.

A set consisting of values that support the alternative hypothesis and lead to rejecting the null hypothesis is called the rejection region.

In a two-tailed test for the population mean, the null hypothesis will be rejected at level of significance if which of the following conditions holds for the value of the test statistic z?

In formulating the null and alternative hypotheses, which of the following would be an acceptable null hypothesis?

The probability of correctly rejecting a false null hypothesis equals and is called the power of the hypothesis test.

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

What is the first step in hypothesis testing?

The width of a confidence interval estimate for a proportion will be narrower for 90% confidence than for 95% confidence.

In testing the difference between two population means using two independent samples, the population standard deviations were assumed to be known and the calculated test statistic equalled 2.56. If the test was two-tailed and a 5% level of significance had been specified, what would be the most appropriate conclusion from the findings?

A quality control officer tests bottles of shampoo to see if the filling machines are putting the proper amount in each bottle. After testing a sample of bottles, the quality control officer decides to leave the filling machines operating. However, the filling machines are not operating properly. Which type of error, if any, did the quality control officer commit?

A professor of mathematics refutes the claim that the average student spends 4.5 hours studying for the final comprehensive exam. To test the claim, she should use the hypothesis , .

Two independent samples of sizes 40 and 50 are randomly selected from two populations to test the difference between the population means . Which of the following best describes the sampling distribution of the sample mean difference ?

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.