A food company is concerned about recent criticism of the sugar content of their

Question

A food company is concerned about recent criticism of the sugar content of their children's cereals. The data show the sugar content (as a percentage of weight) of several national brands of children's and adults' cereals. Complete parts a through d. Full data set Children's cereal: 41, 57, 45.1, 44, 52.5, 48.5, 53.7, 40.8, 42.4, 44.3, 46.1, 44, 37.9, 59.4, 47.5, 50.2, 36.2, 57, 43.1, 31.7 Adults' cereal: 23.8, 27.7, 0.4, 9.4, 1.6, 24.9, 19.8, 14.5, 24.5, 7.2, 8.7, 14.3, 16.3, 10.9, 4.6, 18.5, 0.5, 2.5, 2.2, 6.3, 13.6, 1.9, 2.6, 3, 9.5, 1.2, 17.1, 6.6, 16.5, 13.6 (b) Check the conditions. Which of the following conditions are satisfied for the given data? Select all that apply. Randomization condition Nearly normal condition Independent groups assumption Find the 95% confidence interval for the positive difference in means. The 95% confidence interval is (grams, grams). (Round to two decimal places as needed.)

Explanation / Answer

Calculating the means of each group,              
              
X2 =    10.80666667          
X1 =    67.945          
              
Calculating the standard deviations of each group,              
              
s2 =    8.229464864          
s1 =    98.43073694          
              
Thus, the standard error of their difference is, by using sD = sqrt(s1^2/n1 + s2^2/n2):              
              
n2 = sample size of group 1 =    30          
n1 = sample size of group 2 =    20          
Thus, df = n1 + n2 - 2 =    48          
Also, sD =    22.06100561          
              
      
              
For the   0.95   confidence level, then      
              
alpha/2 = (1 - confidence level)/2 =    0.025          
t(alpha/2) =    2.010634758          
              
lower bound = [X1 - X2] - t(alpha/2) * sD = 101.494958          
upper bound = [X1 - X2] + t(alpha/2) * sD = 12.78170867          
              
Thus, the confidence interval is              
              
( 12.78170867,   101.494958 ) [ANSWER]

*****************************************************

Hi! If you use another method/formula in calculating the degrees of freedom in this t-test, please resubmit this question together with the formula/method you use in determining the degrees of freedom. That way we can continue helping you! Thanks!

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.