Scalability Challenges in MPI Implementations
This content explores the scalability challenges faced by MPI implementations on million-core systems. It discusses factors affecting scalability, performance issues, and ongoing efforts to address scalability issues in the MPI specification.
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Testing a Claim Lesson 8.4 Significance Tests for a Proportion Statistics and Probability with Applications, 3rdEdition Starnes & Tabor Starnes & Tabor Statistics and Probability with Applications, 3rd Edition Bedford Freeman Worth Publishers Bedford Freeman Worth Publishers
Significance Tests for a Proportion Learning Targets After this lesson, you should be able to: After this lesson, you should be able to: Learning Targets Use the four-step process to perform a one-sided significance test about a population proportion. Calculate the P-value for a two-sided significance test about a population proportion using Table A or technology. Use the four-step process to perform a two-sided significance test about a population proportion. Statistics and Probability with Applications, 3rd Edition 2 2
Significance Tests for a Proportion To perform a significance test, we state hypotheses, check conditions, calculate a test statistic and P-value, and draw a conclusion in the context of the problem. The four-step process is ideal for organizing our work. How to Use the Four-Step Process: Significance Tests STATE: State the hypotheses you want to test and the significance level, and define any parameters you use. PLAN: Identify the appropriate inference method and check conditions. DO: If the conditions are met, perform calculations. Find the sample statistic. Calculate the standardized test statistic. Find the P-value. CONCLUDE: Make a conclusion about the hypotheses in the context of the problem. Statistics and Probability with Applications, 3rd Edition 3 3
Significance Tests for a Proportion The P-value in a one-sided test about a population proportion is the area in one tail of a standard normal distribution the tail specified by H a. In a two-sided test, the alternative hypothesis has the form H a: p = p0. The P-value in such a test is the probability of getting a sample proportion as far as or farther from p0 in either direction than the observed sample proportion, assuming the null hypothesis is true. As a result, you have to find the area in both tails of a standard normal distribution to get the P-value. NOTE: when you determine P make sure you account for both ends of the probability. Statistics and Probability with Applications, 3rd Edition 4 4
Significance Tests for a Proportion The result of a significance test begins with a decision to reject H0 or fail to reject H0. When we reject H0, we re left wondering what the actual proportion p might be. A confidence interval might shed some light on this issue. In the previous example, the sample proportion was 0.68. A 95% confidence interval for p is This interval gives the values for p that are plausible based on the sample data. Note that the null value of p = 0.59 is not a plausible value of the parameter. So the 95% confidence interval and the two-sided test at the = 0.05 significance level give consistent results. Statistics and Probability with Applications, 3rd Edition 5 5
LESSON APP 8.4 Who feels job stress? A news report claims that 75% of restaurant employees feel that work stress has a negative impact on their personal lives. Managers of a large restaurant chain wonder if this claim is valid for their employees. A random sample of 100 employees finds that 68 answer Yes when asked, Does work stress have a negative impact on your personal life? Do these data provide convincing evidence at the = 0.10 level that the proportion of all employees in this chain who would say Yes differs from 0.75? Statistics and Probability with Applications, 3rd Edition 6 6
Significance Tests for a Proportion Learning Targets Learning Targets Seatwork/Homework: After this lesson, you should be able to: After this lesson, you should be able to: Use the four-step process to perform a one-sided significance test about a population proportion. Calculate the P-value for a two-sided significance test about a population proportion using Table A or technology. Use the four-step process to perform a two-sided significance test about a population proportion. Lesson 8.4 Seatwork/Homework Pg. 527 #1, 4, 5, & 8. Statistics and Probability with Applications, 3rd Edition 7 7
