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Statistical Analysis of Hypothesis Testing and Confidence Intervals: Case Studies and Calculations

Application of hypothesis testing and confidence intervals in case studies.

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    Statistical Analysis of Hypothesis Testing and Confidence Intervals: Case Studies and Calculations This is a two part assignment that will be submitted within one document. (read Jackson chap 8 & 10 and Torchim 293 - 308) Part I Part I checks your understanding of key concepts from Jackson and Trochim & Donnelly. Answer the following questions: 1. Jackson even - numbered Chapter exercises (pp. 220 - 221; 273 - 275) The producers of a new toothpaste claim that it prevents more cavities than other brands of toothpaste. A random sample of 60 people used the new toothpaste for 6 months. The mean number of cavities at their next checkup is 1.5. In the general population, the mean number of cavities at a 6 - month checkup is 1.73 (Ƒ = 1.12). a. Is this a one - or two - tailed test? This will be a one - tail test because the test is to show that a new toothpaste prevents more cavities than other brands of toothpaste (in this case the mean from the general population). b. What are H0 and Ha for this study? 𝐻 0 : πœ‡ Μ‚ = πœ‡ 0 , or πœ‡ Μ‚ = 1 . 5 of new tooth paste is equal to πœ‡ 0 = 1 . 73 of the general population . 𝐻 ΰ―” : πœ‡ Μ‚ > πœ‡ 0 T or πœ‡ Μ‚ = 1 . 5 of new tooth paste is greater than πœ‡ 0 = 1 . 73 of the general population. c. Compute z obt 𝑍 π‘œπ‘π‘‘ = π‘₯ Μ… βˆ’ πœ‡ 0 𝜎 √ 𝑛 ΰ΅— = 1 . 5 βˆ’ 1 . 73 1 . 12 √ 60 ΰ΅— = βˆ’ 0 . 23 0 . 1446 = βˆ’ 𝟏 . πŸ“πŸ—πŸŽπŸ• d. What is zcv? 𝑍 ΰ―–ΰ―© = 𝑍 ΰ―” = 𝑍 0 . 05 = 𝟏 . πŸ”πŸ’πŸ“ e. Should H0 be rejected? What should the researcher conclude? No the H o should not be rejected. At Ξ± =0.05, the researcher should conclude that the new tooth paste does not prevent more cavities than other brands of toothpaste. f. Determine the 95% confidence interval for the population mean, based on the sample mean. The 95% confidence interval is:

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