Theaverage for group A =6.3
Theaverage for group B = 5.777778
Thestandard deviation of group A=0.2739
Thestandard deviation of group B=0.2108
Thevariance for group A= 0.075
Thevariance for group B=0.044444
Valueof the t-test =3.955
Ifthe t critical,for df =16, sig.=0.05 and two tail test = 2.120 then the t statisticin this study which is 3.955 is greater than the t-critical and hencewe reject the null hypothesis and conclude that group A and group Bare different(Chong et al., 2008).
a).Z score=(X-U)/ Sqrt (Variance) where X is the test sample mean, U isthe population mean.
b).I use Z critical=1.96 (two tails) for my comparison.
TheZ score of 0.3182 is less than the Z critical of 1.96 hence we failto reject the null hypothesis and conclude that the value of 123.5mg/dL is not significantly different from the limit for prediabeteshistorically expected of 120 mg/dL.
C)Ifthe obtained results is higher than the historically expected valuethen the Zscore had to be greater than the Z critical for one toreject the null hypothesis and conclude that value is different fromthe historically expected value.
d).The group should be not considered prediabetes and deserves a propertreatment since the groups average glucose is not higher than thehistorically expected limit for prediabetes of 120mg/dl.
Chong,T. T. L., Hinich, M. J., Liew, V. K. S., & Lim, K. P. (2008).Time series test of nonlinear convergence and transitionaldynamics. EconomicsLetters, 100(3),337-339.