Question

The Table shows the data observations of nerve conductivity speeds. Healthy subjects Nerve disorder subjects уі 1. Calculate the mean and standard deviation of each data set. Use notations i and y for the means and Sx and sy for the standard deviations. 2. Perform a two-sided hypothesis t-test to establish whether the nerve conductivity speeds are different for the two groups of subjects. Ho: Ha=UB Ha: uA È UB To answer this question: a) Calculate the degrees of freedom, v. b) Calculate the 99% confidence interval. Use the Table of the t distribution to find the critical point ta/2,v (use v= 30). 52.20 53.81 53.68 54.47 54.65 52.43 54.43 54.06 52.85 54.12 54.17 55.09 53.91 52.95 54.41 54.14 55.12 53.35 54.40 53.49 52.52 54.39 55.14 54.64 53.05 54.31 55.90 52.23 54.90 55.64 54.48 50.68 47.49 51.47 48.47 52.50 48.55 45.96 50.40 45.07 48.21 50.06 50.63 44.99 47.22 48.71 49.64 47.09 48.73 45.08 45.73 44.86 50.18 52.65 48.50 47.93 47.25 53.98 (8 –5 –ta/2.0V* +3, 6–+ta/2vV+3) c) What is your conclusion? 52.89

Thank you

Answer 1

The step-by-step instructions to obtain two-sample t-test using Minitab 18: * Type the variables Healthy subjects(x) and Nerve disorder subjects(yi) into the columns C1 and C2 of the Minitab 18 worsheet. * Choose the Stat → Basic statistics → 2-sample t. * Choose Each sample in its column. * Select the columns C1 and C2 into the variables box. * Choose the confidence level 99. * Choose the Hypothesized difference:0.0. * Choose the Alternative hypothesis: Difference + Hypothesized difference. * Click ok. The two-sample t-test of the population mean using Mintab18:

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Two-Sample T-Test and Cl: Healthy subjects, Nerve disorder subjects Method He: mean of Healthy subjects Pz: mean of Nerve disorder subjects Difference: pla - Ha Equal variances are assumed for this analysis. Descriptive Statistics Sample N Healthy subjects 32 Nerve disorder subjects 27 Mean StDev SE Mean 53.994 0.974 0.17 48.59 2.49 0 .48 Estimation for Difference Pooled 99% CI for Difference StDev Difference 5.401 1.828 (4.127, 6.674) Test Null hypothesis Ho: 41 - = 0 Alternative hypothesis Hi Ho - H2 = 0 T-Value DF P-value 11.30 570.000

Step1: Let 41 and 4 be the population means and let x, and xy be the means of the respective samples. The sample statistics is of the Two-sample t-test output of the Minitab 18: Samplel: 14 = 32, X = 53.99438, 5, = 0.9735. Sample2:n, = 27, 13 = 48.5937, s, = 2.489714. The level of significance is a =0.01. Step2: State the null and alternative hypotheses. The null and alternative hypotheses are, respectively. We need to use the two-tailed test. HO:HA = 42 Versus H:HA 743 Step 3: Select the distribution to use. Here, the two samples are independent, I and J, are unknown but equal, and the sample sizes are small but both populations are normally distributed. Hence, all conditions are satisfied. Consequently, we will use the t - distribution - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Step4: Determine the rejection and non-rejection regions: The # sign in the alternative hypothesis indicates that the test is two-tailed. The significance level is 0.01. The degrees of freedom is v= 74 +n, -2 = 32+27-2 = 59-2 = 57 v=157 Therefore, the degrees of freedom is v= 57 Step 5: The critical value of t for df = 57 and 0.01 area of the two-tails of the i-distribution curve are +2.66487. - - - - - - - - -

(b) Step 6: The 99% confidence interval for the mean difference between the two population means is 2 s2 (x-7)+tamine 10.947703 6.198678 =(x-7)/2.777, +79-2V 32 ' 27 =(x-7)+1001232+27-2 V0.029616+0.229581 =(x-7)+10005,39-2 V0.259196 =(x-7)+60005.57 (0.509113) =(53.99438-48.5937)+2.66487(0.509113) = 5.400671-1.356721 = (4.04395,6.757392) (x-7)+1/25 - 4.044 34-44 16.657 Step7: Interpretation: We can be 99% confident that the true difference between the population means is between 4.044 and 6.657 - - - - - - - - - - - - - - - - - - - - - (c) Conclusion: Since, the digit 'O' is not contained in the confidence interval calculated of the part(b). We reject the null hypothesis H, There is sufficient evidence to conclude that the difference between the population means is significant at the 1% level of significance.