6. What is a rejection region? What is a confidence level? What is a confidence
ID: 2926721 • Letter: 6
Question
6. What is a rejection region? What is a confidence level? What is a confidence interval? Discuss how the three concepts are related to each other. Provide original examples throughout your discussion. (5 pts) 7. What two characteristics of a variable also affect which statistical test should be used? (2 pts) 8. Given the following information, would your decision be to reject or fail to reject the null hypothesis? Setting the level of significance at.05 for decision making, provide an explanation for your conclusion. (6 pts) a. The null hypothesis that there is no relationship between the type of music a person listens to and his crime rate (px.05) b. The null hypothesis that there is no relationship between the amount of coffee consumption and GPA (p=.62) c. The null hypothesis that there is a negative relationship between the number of hours worked and level of job satisfaction (p-.049) 9. What does chance have to do with testing the research hypothesis for significance? (1 pt)Explanation / Answer
6. Rejection Region: For a hypothesis test, a researcher collects sample data. From the sample data, the researcher computes a test statistic. If the statistic falls within a specified range of values, the researcher rejects the null hypothesis . The range of values that leads the researcher to reject the null hypothesis is called the region of rejection.
For example, a researcher might hypothesize that the population mean is equal to 10. To test this null hypothesis, he/she could collect a random sample of observations and compute the sample mean. If the sample mean is close to 10 (say, between 9 and 11), the researcher might decide to accept the hypothesis. In this example, the region of rejection would be the range of values that are less than 9 or greater than 11. If the sample mean falls in this range, the researcher would reject the null hypothesis.
A confidence level refers to the percentage of all possible samples that can be expected to include the true population parameter. For example, suppose all possible samples were selected from the same population, and a confidence interval were computed for each sample. A 95% confidence level implies that 95% of the confidence intervals would include the true population parameter.
Confidence interval gives an estimated range of values which is likely to include an unknown population parameter, the estimated range being calculated from a given set of sample data.If repeated samples were taken and the 95%confidence interval was computed for each sample, 95% of the intervals would contain the population mean. A 95% confidence interval has a 0.95 probability of containing the population mean. 95% of the population distribution is contained in theconfidence interval.
Rejection region, confidence level, and confidence intervals, are different ways to represent the probability that the observed data is representative of the actual data, or in the case of a rejection region, are not representative of said data.
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