Weights of Vacuum Cleaners Upright vacuum cleaners have either a hard body type or a soft body type. Shown are the weights in pounds of a randomsample of each type. Find the 90% confidence interval for the difference of the means. Assume the variables are normally distributed and the variances areunequal. Round the sample mean and sample standard deviation to two decimal places and the final answers to at least one decimal place.2120Hard body types17 152318163861715<₂-₂<Send data to Excel201716 1117 172416XSoft body typesUse ₁ for the mean weight of the hard body type.12 15 141718 13S

Followings are the Explanation of the question Use the Excel and calculate the Sample mean and Sample standard deviation for the two groupsConstruct the 90% confidence interval for the mean difference when the Variances are unequal Construct the 90% confidence interval for the difference between the population means μ1-μ2 when population standard deviation are not known. Provided Data : Sample mean 1 (X1) = 17.5 Sample Standard Deviation 1 (S1) = 2.50 Sample Size 1 (n1)= 16 Sample mean 2 (X2) = 15.5 Sample Standard Deviation 2 (s2) = 3.91 Sample Size 2 (n2)= 9 Find the Level of significance α 100(1-alpha) %= 90% 100(1-alpha) = 100 (1-alpha) = 90/100 (1-alpha) = 0.90 alpha = 1-0.90 alpha = 0.10 Calculate the Degrees of Freedom and Corresponding Critical value using t table we assume that the population variances are equal, so then the number of degrees of freedom are df = n1+n2-2= 16+ 9- = 25-2=23 The critical value for α=0.10 anddf=23 degrees of freedom is tc=t(1-α/2;n-1)=1.7852 Or use the Excel formula :- TDIST.S.INV(1-0.10/2) Calculate Pooled Standard Error :- SE=√(s12/n1+s22/n2)SE=√(2.52/16+3.912/9)SE=1.4454 Construct the 99% confidence interval for the difference between the population means C.I=[(X¯1-X¯2)-TC*Se,(X¯1-X¯2)+TC*Se)]C.I=[(17.5-15.5)-1.7852*1.4454,(17.5-15.5)+1.7852*1.4454]C.I=(-0.6,4.6) Therefore, the 90 % confidence interval for the difference between the population means -0.6<μ1-μ2<4.6