Recent questions in Significance tests
Significance tests

Suppose that you want to perform a hypothesis test based on independent random samples to compare the means of two populations. You know that the two distributions of the variable under consideration have the same shape and may be normal. You take the two samples and find that the data for one of the samples contain outliers. Which procedure would you use? Explain your answer.

Significance tests

Suppose that you want to perform a hypothesis test to compare four population means, using independent samples. In each case, decide whether you would use the one-way ANOVA test, the Kruskal-Wallis test, or neither of these tests. Preliminary data analyses of the samples suggest that the four distributions of the variable a. are not normal but have the same shape. b. are normal and have the same shape.

Significance tests

In the treatment of critically ill patients, teamwork among health care professionals is essential. What is the level of collaboration between nurses and resident doctors working in the intensive care unit (ICU)? This was the question of interest in an article published in the Journal of Advanced Nursing (Vol. 67, 2011). Independent samples of 31 nurses and 46 resident doctors, all working in the ICU, completed the Baggs Collaboration and Satisfaction about Care Decisions survey. Responses to all questions were measured on a 7-point scale, where $$1 =$$ never and $$7 =$$ always. The data for the following two questions (simulated from information provided in the article) are listed above. a. Conduct a nonparametric test (at $$\alpha=05\ \alpha=05$$) to compare the response distributions for nurses and doctors on Question 4. Practically interpret the result. b. Conduct a nonparametric test (at $$\alpha=05\ \alpha=05$$) to compare the response distributions for nurses and doctors on Question 5. Practically interpret the result. Question 4: Physicians and nurses cooperate in making decisions. Nurses:1 1 1 1 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 4 5 5 5 5 5 5 5 7 7 Doctors:1 1 1 1 1 1 1 2 2 2 3 3 3 3 3 3 3 3 3 3 4 4 5 5 5 5 5 5 5 5 5 5 5 5 5 6 6 6 6 6 6 7 7 7 7 7 Question 5: In making decisions, both nursing and medical concerns about patients' needs are considered. Nurses:1 1 2 2 2 2 3 3 3 3 33 3 3 3 4 4 4 4 4 4 5 5 5 5 5 5 5 5 6 6 7 Doctors:2 2 2 2 2 3 3 3 4 4 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 6 6 6 6 6 6 6 6 6 6 7 7 7 7 7 7 7 7

Significance tests

Although tea is the world’s most widely consumed beverage after water, little is known about its nutritional value. Folacin is the only B vitamin present in any significant amount in tea, and recent advances in assay methods have made accurate determination of folacin content feasible. Consider the accompanying data on folacin content for randomly selected specimens of the four leading brands of green tea. Brand 1234amp; Observations amp;7.9amp;5.7amp;6.8amp;6.4amp;6.2amp;7.5amp;7.5amp;7.1amp;6.6amp;9.8amp;5.0amp;7.9amp;8.6amp;6.1amp;7.4amp;4.5amp;8.9amp;8.4amp;5.3amp;5.0amp;10.1amp;amp;6.1amp;4.0amp;9.6amp;amp;amp; (Data is based on “Folacin Content of Tea,” J. Amer. Dietetic Assoc., 1983: 627–632.) Does this data suggest that true average folacin content is the same for all brands? a. Carry out a test using $$\alpha:=.05$$ via the P-value method. b. Assess the plausibility of any assumptions required for your analysis in part (a). c. Perform a multiple comparisons analysis to identify significant differences among brands.

Significance tests

For a test of $$H_{0}:\ p=0.5,$$ the z test statistic equals 1.74. Find the p-value for $$H_{a}:\ p>0.5$$. a) 0.0446 b) 0.0409 c) 0.892 d) 0.9591 e) 0.0818 f) 0.9554

Significance tests

Find the margin of error for the given values of c,s, and n. c=0.95, s=2.2, n=64

Significance tests

The means of the number of revolutions per minute of two competing engines are to be compared. Thirty engines are randomly assigned to be tested. Both populations have normal distributions. Table 10.9 shows the result. Do the data indicate that Engine 2 has higher RPM than Engine 1? Test at a 5% level of significance. EngineSample Mean Number of RPMPopulation Standard Deviation 11,50050 21,60060 Table 10.9

Significance tests

To explain:Whether the samples are independent or dependent.

Significance tests

If a report states that certain data were used to reject a given hypothesis, would it be a good idea to know what type of test (one-tailed or two-tailed) was used? Explain.

Significance tests

To state:The null and alternative hypothesis.

Significance tests

To state:The null and alternative hypotheses.

Significance tests

Find the slope of the regression. Find the t-statistic for testing the slope. Find the p-value for testing the slope.

Significance tests

To explain:The purpose of the study.

Significance tests

Check Requirements What sampling distribution will you use? What assumptions are you making? What is the value of the sample test statistic?

Significance tests

To describe:How would you test the representative's claim and also identify the type of the test.

Significance tests

In there a relationship between confidence intervals and two-tailed hypothesis tests? The answer is yes. Let c be the level of confidence used to construct a confidence interval from sample data. Let * be the level of significance for a two-tailed hypothesis test. The following statement applies to hypothesis tests of the mean: For a two-tailed hypothesis test with level of significance a and null hypothesis $$H_{0} : \mu = k$$ we reject Ho whenever k falls outside the $$c = 1 — \alpha$$ confidence interval for $$\mu$$ based on the sample data. When A falls within the $$c = 1 — \alpha$$ confidence interval. we do reject $$H_{0}$$. For a one-tailed hypothesis test with level of significance Ho : $$\mu = k$$ and null hypothesiswe reject Ho whenever A falls outsidethe $$c = 1 — 2\alpha$$ confidence interval for p based on the sample data. When A falls within the $$c = 1 — 2\alpha$$ confidence interval, we do not reject $$H_{0}$$. A corresponding relationship between confidence intervals and two-tailed hypothesis tests is also valid for other parameters, such as p, $$\mu1 — \mu_2,\ and\ p_{1}, - p_{2}$$. (a) Consider the hypotheses $$H_{0} : \mu_{1} — \mu_{2} = O\ and\ H_{1} : \mu_{1} — \mu_{2} \neq$$ Suppose a 95% confidence interval for $$\mu_{1} — \mu_{2}$$ contains only positive numbers. Should you reject the null hypothesis when $$\alpha = 0.05$$? Why or why not?

Significance tests

To describe:It is possible that the given claim is true or not. To describe:The questions that should ask about how the data were collected.

Significance tests

Critical Thinking: One-Tailed versus Two-Tailed Tests For the same data and null hypothesis, is the P-value of a one-tailed test (right or left) larger or smaller than that of a two-tailed test? Explain.

Significance tests