Question

A company tested 11 random brands of vanilla yogurt and found the number of calories per serving given below.​ (Note that more than 110 different brands of vanilla yogurt​ exist.) Complete parts a through c. 140 160 140 110 120 120 170 160 100 120 80 Is the Independence Assumption​ met? Is the Randomization Condition met or is the sample suitably​ representative? Is the​ 10% Condition​ met? Is the Nearly Normal Condition​ met? ​b) Find a​ 95% confidence interval for the average calorie content of vanilla yogurt per serving. ​c) Interpret this interval for someone looking to buy yogurt. Choose the correct answer below.

Answer 1

a)

We can assume that the independence condition is satisfied.

Randomization Condition is satisfied because the brands has been selected randomly.

The 10% condition is satisfied because the sample is less than 10% of the population.

The nearly normal condition is satisfied since there is no major deviation from normality.

b)

∑x = 1420  

∑x² = 191000  

n = 11  

Mean, x̅ = Ʃx/n = 1420/11 = 129.0909

Standard deviation, s = √[(Ʃx² - (Ʃx)²/n)/(n-1)] = √[(191000-(1420)²/11)/(11-1)] = 27.7325

95% Confidence interval :  

At α = 0.05 and df = n-1 = 10, two tailed critical value, t-crit = T.INV.2T(0.05, 10) = 2.228

Lower Bound = x̅ - t-crit*s/√n = 129.0909 - 2.228 * 27.7325/√11 = 110.46

Upper Bound = x̅ + t-crit*s/√n = 129.0909 + 2.228 * 27.7325/√11 = 147.722

c)

We can be​ 95% confident that the interval contains the true mean number of calories per serving of yogurt.