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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 Studiesand CalculationsThis is a two partassignment that will be submitted within one document.(read Jackson chap 8 & 10and Torchim 293-308)Part IPart 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 attheir next checkup is 1.5. In the general population, the mean number of cavities at a 6-month checkupis 1.73 (ร†ยก = 1.12).a.Is this a one-or two-tailed test?This will be aone-tail test because the test is to show thata new toothpaste prevents morecavities than other brands of toothpaste (in this case the mean from the general population).b.What are H0 and Ha for this study?๐ป0:๐œ‡ฬ‚=๐œ‡0, or๐œ‡ฬ‚=1.5ofnew tooth pasteis equal to๐œ‡0=1.73of thegeneral population.๐ปเฏ”:๐œ‡ฬ‚>๐œ‡0T or๐œ‡ฬ‚=1.5of new tooth paste is greater than๐œ‡0=1.73of the general population.c.Compute z obt๐‘๐‘œ๐‘๐‘ก=๐‘ฅฬ…โˆ’๐œ‡0๐œŽโˆš๐‘›เต—=1.5โˆ’1.731.12โˆš60เต—=โˆ’0.230.1446=โˆ’๐Ÿ.๐Ÿ“๐Ÿ—๐ŸŽ๐Ÿ•d.What is zcv?๐‘เฏ–เฏฉ=๐‘เฏ”=๐‘0.05=๐Ÿ.๐Ÿ”๐Ÿ’๐Ÿ“e.Should H0 be rejected? What should the researcher conclude?No the Hoshould not be rejected. Atฮฑ=0.05, the researcher should conclude that thenew toothpaste does not prevent more cavities than other brands of toothpaste.f.Determine the 95% confidence interval for the population mean, based on the samplemean.The 95% confidence interval is:

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