This page provides solutions and examples for Biostatistics assignments, including calculating confidence intervals, critical values, effect size, and more. It also includes a comparison of risk-taking behavior between boys and girls using side-by-side box plots.
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~1~ Biostatistics Assignment
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~2~ ANS:Confidence interval for mean is x − ±t0.95 s √n, wherex − =2998gis the mean ands=800gis the standard deviation of the sample,n=49is the sample size, andtαis the value of the statistic forgivenconfidencelevel(tα=±2.01for95%CI,twotailed).Theconfidenceintervalis [2998−2.01∗800 √49,2998+2.01∗800 √49] =[2768.29,3227.71]for 95% confidence level. From the sampling attributes it is assessed that there is a 95% chance that average birth weight of SIDS cases will be within the limits of confidence interval. ANS: Sample mean = 7.40+7.36+7.45 3=7.40, population standard deviation is σ = 0.070. As titermeasurementfollowsnormaldistribution,95%confidenceintervaliscalculatedas x − ±z0.95 σ √n
~3~ Hence, the 95% confidence interval is [7.40−1.96∗0.07 √3,7.40+1.96∗0.07 √3]=[7.32,7.48] where z0.95=1.96. ANS:a (False), b (False), c (True) ANS:Critical value of t-statistics for α = 0.05 are as follows: Right-tailtcrit=1.725 (degrees of freedom (DOF) = n -1 = 20), left-tailtcrit= - 1.725 (degrees of freedom (DOF) = n -1 = 20). Therefore, P (tstat≤−1.725) = 0.05 and P (tstat≥−1.725) = 0.05. Two-tailcriticalvalueoft-statisticsistcrit=±2.086(DOF=20),whichimplies P (−2.086≤tstat≤2.086) = 0.05.
~4~ ANS:Both z-procedure and t-procedure follows Gaussian distribution. But, in absence of the knowledge of population standard deviation, sample standard deviation is used for estimating the population parameters. Sample standard deviation is known to follow t-distribution instead of z- procedure, and for estimating population parameter t-procedure is followed. ANS:Sample size:n= 26 boys, sample mean = 63.8 inches, and sample standard deviation = 3.1 inches. Population standard deviation is not known, and sample S.D is known to follow t-distribution. Degrees of freedom = 26 – 1 =25. Hence, tcrit=2.086 for two tail implies that the 95% confidence interval is estimated as x − ±t0.95 s √n. The calculated 95% confidence interval for the mean height of the population is as follows: - [63.8−2.086∗3.1 √26,63.8+2.086∗3.1 √26]=[62.53,65.07]
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~5~ Average population height is expected to be within 62.53 inches and 65.07 inches. ANS:a. Paired Samples b. Independent Samples c. Single Sample ANS:The null hypothesis: H0:μd=0and the alternate hypothesis HA:μd≠0 The sample size is n=(Z1−α 2 +Z1−β EffectSize) 2 , where Z1−α 2= 1.96 for α = 0.05 (two-sided) andZ1−β= 1.282 for 90% power (Williams, 2017).
~6~ The effect size = |Δμ| σ=0.25 0.67=0.37, and n=(Z1−α 2 +Z1−β EffectSize) 2 =(1.96+1.282 0.37) 2 =76.78 Therefore, sample size of 77 has 90% power at α = 0.05 (two-sided). ANS:Back-to-back steam and Side-by-side box plots can compare two independent groups of quantitative data. ANS:A measure of index of risk-taking behavior in boys and girls has been explored utilizing group differences with side-by-side box plots.
~7~ 6 08 01 0 01 2 01 4 0 Index_BoysIndex_Girls Figure1: Side-by-side Box Plot for index of risk-taking behavior The index for boys is left skewed, whereas index for girls is slightly right skewed. Median of girls is higher than that of the boys. From the box plots an outlier index value of 125 is clearly visible for the boys. Risk taking attitude is visibly greater for the girls compared to that of the boys (Norman, & Streiner, 2008). References Norman, G. R., & Streiner, D. L. (2008).Biostatistics: The Bare Essentials. PMPH-USA. Williams, B. (2017).Biostatistics : Concepts and Applications for Biologists. CRC Press. https://doi.org/10.1201/9781315150314