Question

A report included the following information on the heights (in.) for non-Hispanic white females Sample Sample Std. Error Mean Mean Age Size 20-39 64.7 867 0.09 60 and older 934 63.1 0.11 (a) Calculate a confidence interval at confidence level approximately 95% for the difference between population mean height for the younger women and that for the older women. (Use n39-H0 and older) 2.01 Interpret the interval. OWe are 95% confident that the true average height of younger women is less than that of older women by an amount within the confidence interval. OWe are 95 % confident that the true average height of younger women is greater than that of older women by an amount outside the confidence interval We are 95% confident that the true average height of younger women is greater than that of older women by an amount within the confidence interval. We cannot draw a conclusion from the given information. (b) Let denote the population mean height for those aged 20-39 and A, denote the population mean height for those aged 60 and older. Interpret the hypotheses Hi u, - i, = 1 and H: ,- 2 > 1. O The null hypothesis states that the true mean height for older women is more than 1 inch higher than for younger women. The alternative hypothesis states that the true mean height for older women is 1 inch higher than for younger women O The null hypothesis states that the true mean height for younger women is more than higher than for older women. inch higher than for older women. The alternative hypothesis states that the true mean height for younger women is 1 inch O The null hypothesis states that the true mean height for older women is 1 inch higher than for younger women. The alternative hypothesis states that the true mean height for older women is more than 1 inch higher than for younger women The null hypothesis states that the true mean height for younger women is 1 inch higher than for older women. The alternative hypothesis states that the true mean height for younger women is more than 1 inch higher than for older women. Carry out a test of these hypotheses at significance level 0.001. Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to four decimal places. P-value

Answer 1

a)

Level of Significance ,    α =    0.05          
z-critical value =    Z α/2 =    1.960   [excel function =normsinv(α/2) ]      
                  
std error , SE =    √(σ1²/n1+σ2²/n2) =    0.1421          
margin of error, E = Z*SE =    1.960   *   0.142   =   0.2786
                  
difference of means = x̅1 - x̅2 =    64.7   -   63.1   =   1.600
confidence interval is                   
Interval Lower Limit= (x̅1 - x̅2) - E =    1.600   -   0.279   =   1.3214
Interval Upper Limit= (x̅1 - x̅2) + E =    1.600   +   0.279   =   1.8786

interpretation: option C)

b) option D)

difference in sample means = x̅1 - x̅2 =    64.7   -   63.1   =   1.6
                  
std error , SE =    √(σ1²/n1+σ2²/n2) =    0.1421          
                  
Z-statistic = ((x̅1 - x̅2)-µd)/SE =    1.6   /   0.1421   =   4.22
                  
  
p-value =        0.0000 [excel function =NORMSDIST(z)]      

c) option A)

d) option B)