Statistics Practice For Final: Be Sure To Review The Followi

Statistics Practice For Finalbe Sure To Review The Following And Have

Statistics practice for final Be sure to review the following and have this information handy when taking Final GHA: · Calculating z alpha/2 and t alpha/2 on Tables II and IV · Find sample size for estimating population mean. Formula 8.3 p. 321 OCR. · Stating H0 and H1 claims about variation and about the mean. Chapter 9 OCR. · Type I and Type II errors p. 345 OCR. · Confidence Interval for difference between two population means. Chapter 10 OCR p. 428 · Pooled sample standard deviation. Chapter 10 OCR p. 397 · What do Chi-Square tests measure? How are their degrees of freedom calculated? Chapter 12 OCR · Find F test statistic using One-Way ANOVA.xls Be sure to enable editing and change values to match your problem. One-Way ANOVA.xls · Find equation of regression line used to predict. To do on Excel, go to a blank worksheet, enter x values in one column and their matching y values in another column. Click Insert – Select Scatterplot. Right click any one of the points (diamonds) on the graph. Left click “Add a Trendline.†Check “Display Equation on Chart†box. Regression equation will appear on chart. Try it here with No. 20 below. Practice Problems Chapter 8 Final Review 1) In which of the following situations is it reasonable to use the z-interval procedure to obtain a confidence interval for the population mean? Assume that the population standard deviation is known. A. n = 10, the data contain no outliers, the variable under consideration is not normally distributed. B. n = 10, the variable under consideration is normally distributed. C. n = 18, the data contain no outliers, the variable under consideration is far from being normally distributed. D. n = 18, the data contain outliers, the variable under consideration is normally distributed. Find the necessary sample size. 2) The weekly earnings of students in one age group are normally distributed with a standard deviation of 10 dollars. A researcher wishes to estimate the mean weekly earnings of students in this age group. Find the sample size needed to assure with 95 percent confidence that the sample mean will not differ from the population mean by more than 2 dollars. Find the specified t-value. 3) For a t-curve with df = 6, find the two t-values that divide the area under the curve into a middle 0.99 area and two outside areas of 0.005. Provide an appropriate response. 4) Under what conditions would you choose to use the t-interval procedure instead of the z-interval procedure in order to obtain a confidence interval for a population mean? What conditions must be satisfied in order to use the t-interval procedure? CHAPTER 8 Answers 1) B .707, 3.) When the population standard deviation is unknown, the t-interval procedure is used instead of the z-interval procedure. The t-interval procedure works provided that the population is normally distributed or the sample is large. Chapter 9 Final Review Classify the hypothesis test as two-tailed, left-tailed, or right-tailed. 5) In the past, the mean running time for a certain type of flashlight battery has been 8.1 hours. The manufacturer has introduced a change in the production method and wants to perform a hypothesis test to determine whether the mean running time has changed as a result. Classify the conclusion of the hypothesis test as a Type I error, a Type II error, or a correct decision. 6) The maximum acceptable level of a certain toxic chemical in vegetables has been set at 0.2 parts per million (ppm). A consumer health group measured the level of the chemical in a random sample of tomatoes obtained from one producer to determine whether the mean level of the chemical in these tomatoes exceeds the recommended limit. The hypotheses are H0 : μ = 0.2 ppm Ha : μ > 0.2 ppm where μ is the mean level of the chemical in tomatoes from this producer. Suppose that the results of the sampling lead to nonrejection of the null hypothesis. Classify that conclusion as a Type I error, a Type II error, or a correct decision, if in fact the mean level of the chemical in these tomatoes is greater than 0.2 ppm. Provide an appropriate response. 7) Robert is conducting a hypothesis test concerning a population mean. The hypotheses are as follows. H0 : μ = 50 Ha : μ > 50 He selects a sample of size 35 and finds that the sample mean is 60. He then does some calculations and finds that for samples of size 35, the standard deviation of the sample means is 3.2. Do you think that he should reject the null hypothesis? Why or why not? The significance level and P-value of a hypothesis test are given. Decide whether the null hypothesis should be rejected. 8) α = 0.01, P-value = 0.002 5 Use a table of t-values to estimate the P-value for the specified one-mean t-test. 9) Two-tailed test, n = 9, t = 3.696 Provide an appropriate response. 10) A hypothesis test for a population mean is to be performed. True or false: The probability of a Type I error is equal to the significance level. CHAPTER 9 Answers 5) Two-tailed 6) Type II error 7) Answers will vary. Possible answer. Yes, he should reject the null hypothesis. If H0 were true, it is not very likely that the sample mean would be as big as 60, since this is more than three standard deviations from 50. So the observed sample mean is inconsistent with the null hypothesis. 8) Reject the null hypothesis. 9) P

Paper For Above instruction

The final exam in statistics encompasses a comprehensive review of essential statistical concepts and procedures. These include understanding how to calculate critical values such as z alpha/2 and t alpha/2 from standard tables, determining the required sample size for estimating a population mean using the specified formulas, and articulating hypotheses concerning population parameters including means and variances. Critical distinctions between Type I and Type II errors in hypothesis testing are vital, along with the ability to interpret confidence intervals, especially for differences between two population means. Calculating pooled sample standard deviations forms part of the analysis for two-sample t-tests, alongside understanding what Chi-Square tests measure and how their degrees of freedom are computed. Additionally, students should be familiar with how to compute the F-test statistic in the context of ANOVA (Analysis of Variance) and how to establish the regression line for prediction purposes using scatterplots and trendline functions in Excel.

Practical scenarios involve choosing the appropriate confidence interval technique (z-interval or t-interval) based on population standard deviation knowledge, sample size, and distribution normality. For example, when the population standard deviation is known and the sample size is small with normally distributed data, the z-interval procedure is suitable. Conversely, for unknown population standard deviation or non-normal data with smaller samples, the t-interval is preferable. The exam also tests knowledge on hypothesis testing procedures, including identifying the nature (two-tailed, left-tailed, right-tailed), and understanding the implications of the p-value in decision-making. Questions may involve assessing the risk of errors, such as Type I or Type II, based on the results of the test and the context of real-world variables like manufacturing times, chemical levels in food, or salaries.

Further, students should demonstrate mastery in conducting two-sample hypothesis tests for means, using pooled t-test methods or separate variances as appropriate, and constructing confidence intervals for the difference between two means. They must also distinguish between independent and paired samples, illustrating their differences with suitable examples. Chi-Square tests for variance assessment or goodness-of-fit involve calculating test statistics and comparing them to critical values for specified degrees of freedom, with attention to normality assumptions. In ANOVA, the F-test evaluates whether multiple group means significantly differ, with interpretations based on the calculated F-statistic and corresponding critical value.

Regression analysis skills include deriving the line of best fit for given data, predicting responses based on predictor variables, and understanding the significance of correlation coefficients for assessing the distribution normality of data. The entire preparation emphasizes applying these concepts through practical problems and interpreting the results correctly, ensuring a full grasp of inferential statistical techniques required for the final assessment.

References

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